EQUADIFF 2003

EQUADIFF 2003
Proceedings of the International Conference on Differential Equations

Hasselt, Belgium, 22 - 26 July 2003

CONTENTS


FRONT MATTER	v
Plenary lectures
THE LAGRANGIAN POINTS OF THE REAL EARTH-MOON SYSTEM ENRIC CASTELLÀ and ÀNGEL JORBA	3
SYNCHRONY VERSUS SYMMETRY IN COUPLED CELLS MARTIN GOLUBITSKY and IAN STEWART	13
THREE-DIMENSIONAL SOLITARY GRAVITY-CAPILLARY WATER WAVES M. D. GROVES	25
MATHER THEORY, WEAK KAM THEORY, AND VISCOSITY SOLUTIONS OF HAMILTON-JACOBI PDE'S VADIM YU. KALOSHIN	39
AN APPLICATION OF NON-SMOOTH MECHANICS IN REAL ANALYSIS P. KREJČÍ	49
CHAOS IN THREE PHYSICAL SYSTEMS R.S. MACKAY	59
MIXED-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS, HOLOMORPHIC FACTORIZATION, AND APPLICATIONS JOHN MALLET-PARET and SJOERD VERDUYN LUNEL	73
COMPETITIVE SYSTEMS WITH THREE SPECIES AND PERIODIC COEFFICIENTS RAFAEL ORTEGA	90
ASYMPTOTIC SYMMETRY OF POSITIVE SOLUTIONS OF PARABOLIC EQUATIONS P. POLÁČIK	99
BIFURCATIONS OF PLANAR VECTOR FIELD UNFOLDINGS ROBERT ROUSSARIE	109
POSITIVITY, CONTINUATION AND NONLINEAR EIGENVALUE PROBLEMS KLAUS SCHMITT	119
TIME SERIES ANALYSIS: SMOOTHED CORRELATION INTEGRALS, AUTOCOVARIANCES, AND POWER SPECTRA FLORIS TAKENS	128
ON POINCARÉ - TRESHCHEV TORI IN HAMILTONIAN SYSTEMS YONG LI and YINGFEI YI	136
Mini-symposia: Computational aspects of differential equations and applications (Org.: B. Krauskopf and K. Lust)
TOWARDS AUTOMATED CHAOS VERIFICATION SARAH DAY, OLIVER JUNGE and KONSTANTIN MISCHAIKOW	157
ELEMENTAL PERIODIC ORBITS OF THE CR3BP: A BRIEF SELECTION OF COMPUTATIONAL RESULTS E. J. DOEDEL, D. J. DICHMANN, J. GALÁN-VIOQUE, H. B. KELLER, R. C. PAFFENROTH and A. VANDERBAUWHEDE	163
THE FORMATION OF SHEAR LAYERS IN A FLUID WITH TEMPERATURE-DEPENDENT VISCOSITY DONALD J. ESTEP, SJOERD M. VERDUYN LUNEL and ROY D. WILLIAMS	169
FROM LOCAL TO GLOBAL ONE-DIMENSIONAL UNSTABLE MANIFOLDS IN DELAY DIFFERENTIAL EQUATIONS B. KRAUSKOPF, K. GREEN and K. ENGELBORGHS	175
A PARALLEL METHOD TO COMPUTE QUASI-PERIODIC SOLUTIONS ÀNGEL JORBA and ESTRELLA OLMEDO	181
A NEWTON–PICARD COLLOCATION METHOD FOR COMPUTING PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS K. LUST and K. VERHEYDEN	184
NUMERICAL STUDY OF MANIFOLD COMPUTATIONS HINKE OSINGA and REZA ROKNI	190
A LIMITED MEMORY BROYDEN METHOD TO SOLVE HIGH-DIMENSIONAL SYSTEMS OF NONLINEAR EQUATIONS BART VAN DE ROTTEN and SJOERD VERDUYN LUNEL	196
COMPUTING CONNECTING ORBITS IN DELAY DIFFERENTIAL EQUATIONS USING DDE-BIFTOOL G. SAMAEY and D. ROOSE	202
Water waves (Org.: M. Groves and M. Haragus)
WAVE-CURRENT INTERACTIONS ADRIAN CONSTANTIN	207
JUSTIFICATION OF THE EQUATIONS FOR THE RESONANT FOUR WAVE INTERACTION GUIDO SCHNEIDER and OLIVER ZINK	213
VISCOUS WATER WAVES IN A BIFURCATION APPROACH AND CONNECTIONS TO INVISCID THEORIES BEN SCHWEIZER	219
Topological and variational methods (Org.: J. Mawhin)
EXISTENCE RESULTS FOR DISCONTINUOUS ORDINARY DIFFERENTIAL EQUATIONS J. ÁNGEL CID and RODRIGO L. POUSO	227
MULTITRANSITION CONNECTIONS FOR FOURTH ORDER EQUATIONS WITH A BISTABLE NONLINEARITY DENIS BONHEURE	230
POSITIVE SOLUTIONS OF A SECOND ORDER SINGULAR ORDINARY DIFFERENTIAL EQUATION D. BONHEURE, J.M. GOMES and L. SANCHEZ	234
RESONANT SYSTEMS WITH PERIODIC NONLINEARITY A. CAÑADA and D. RUIZ	237
SHARP CONDITIONS FOR THE SUPERLINEARITY OF THE SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS Y. A. KLOKOV and F. SADYRBAEV	243
ON THE NUMBER OF BRANCHES OF PERIODIC SOLUTIONS A. KRASNOSEL'SKII and D. RACHINSKII	246
EXISTENCE AND NON-EXISTENCE RESULTS FOR TWO-POINT BOUNDARY VALUE PROBLEMS OF HIGHER ORDER F. M. MINHÓS and I. SANTOS	249
METHOD OF LOWER AND UPPER FUNCTIONS IN IMPULSIVE PERIODIC BOUNDARY VALUE PROBLEMS I. RACHŮNKOVÁ and M. TVRDÝ	252
ALMOST PERIODIC SOLUTIONS OF FORCED SINE-GORDON EQUATIONS AURELIANO M. ROBLES-PÉREZ	258
ISOLATED SETS OF SOLUTIONS OF TWO-POINT BOUNDARY VALUE PROBLEMS AND THEIR INDEXES ROMAN SRZEDNICKI	264
A PRIORI ESTIMATES AND EXISTENCE OF SOLUTIONS FOR NONLINEAR PROBLEMS INVOLVING THE P-LAPLACIAN D. RUIZ	270
Qualitative theory of nonlinear parabolic and elliptic equations (Org.: H. Matano and M. Fila)
ILL POSED PROBLEMS WITH SUPERCRITICAL NONLINEARITIES JOSÉ M. ARRIETA	277
SMOOTH BIFURCATION AND VARIATION OF THE CONTACT SETS FOR AN OBSTACLE PROBLEM J. EISNER, M. KUČERA and L. RECKE	281
IMMEDIATE REGULARIZATION AFTER BLOW-UP M. FILA, H. MATANO and P. POLÁČIK	284
ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS G. V. GRISHINA	290
FLUX CONDITION INDUCED BY CONCENTRATED REACTIONS JOSÉ M. ARRIETA, ANGELA JIMÉNEZ-CASAS and ANíBAL RODRíGUEZ-BERNAL	293
STABILITY ANALYSIS FOR THE CURVATURE-DRIVEN MOTION OF CURVES WITH TRIPLE JUNCTIONS R. IKOTA and E. YANAGIDA	296
SYMMETRY IN ANISOPTROPIC MEDIA B. KAWOHL	301
SMOOTH BIFURCATION AND EXCHANGE OF STABILITY FOR VARIATIONAL INEQUALITIES M. KUČERA, J. EISNER and L. RECKE	307
ON SOME ELLIPTIC EQUATION WITH NONLOCAL NONLINEARITY R. STAŃCZY	310
NONUNIQUENESS IN STRONGLY DEGENERATE DIFFUSION EQUATIONS WITH STRONG ABSORPTION MICHAEL WINKLER	313
Around Hilbert's 16th problem (Org.: Y. Ilyashenko, R. Roussarie and F. Dumortier)
THE USE OF MELNIKOV FUNCTIONS IN MULTI-DIMENSIONAL PARAMETER FAMILIES: ALGEBRAIC CURVES OF MAXIMAL CYCLICITY M. CAUBERGH and F. DUMORTIER	319
QUADRATIC SYSTEMS WITH AN ALGEBRAIC LIMIT CYCLE OF DEGREE 2 OR 4 DO NOT HAVE A LIOUVILLIAN FIRST INTEGRAL J. CHAVARRIGA, H. GIACOMINI and M. GRAU	325
ON A CRITERIUM OF GLOBAL ATTRACTION FOR ORDINARY DIFFERENTIAL EQUATIONS B. COLL, A. GASULL and R. PROHENS	328
GENERALIZED NONLINEAR SUPERPOSITION PRINCIPLES I.A. GARCíA, J. GINÉ and H. GIACOMINI	334
LIMIT SETS OF PLANAR VECTOR FIELDS AND THE VANISHING SET OF INVERSE INTEGRATING FACTORS I. A. GARCÍA and D. S. SHAFER	337
SOME RESULTS ON RIGID SYSTEMS A. GASULL and J. TORREGROSA	340
PERSISTENCE THEOREMS FOR HOLOMORPHIC FOLIATIONS AND KUPKA-SMALE PROPERTY FOR POLYNOMIAL AUTOMORPHISMS OF ℂ² YU. ILYASHENKO	346
COEXISTENCE OF CENTERS AND LIMIT CYCLES IN LIÉNARD SYSTEMS M. SABATINI	354
FROM THE PP-GRAPHICS TO THE FINITENESS PART OF HILBERT'S 16^TH PROBLEM FOR QUADRATIC SYSTEMS HUAIPING ZHU	357
Navier-Stokes equations and reaction diffusion equations (Org.: R. Farwig and M. Wiegner)
REDUCED STOKES EQUATIONS AND BOUNDED H_∞-CALCULUS HELMUT ABELS	365
FLOW AROUND ROTATING OBSTACLES – ANALYSIS OF A SINGULAR INTEGRAL OPERATOR REINHARD FARWIG	371
SOME REMARKS TO REGULARITY OF FLOW OF GENERALIZED NEWTONIAN FLUID PETR KAPLICKÝ	377
FLUIDS WITH PRESSURE DEPENDENT VISCOSITY: PARTIAL REGULARITY OF STEADY FLOWS J. MÁLEK, G. MINGIONE and J. STARÁ	380
LONG-TIME ASYMPTOTICS OF NAVIER-STOKES AND VORTICITY EQUATIONS IN A THREE-DIMENSIONAL LAYER VIOLAINE ROUSSIER	386
A SINGULAR PROBLEM WITH NON-CONSTANT TEMPERATURE - STEADY STATES ANDRZEJ RACZYŃSKI	389
THE STOKES OPERATOR WITH ROBIN BOUNDARY CONDITIONS IN $L_\sigma^\infty (\mathbb{R}_+^n)$ JÜRGEN SAAL	392
ON ANALYTIC PROPERTIES FOR THE STRONG SOLUTIONS TO THE NAVIER-STOKES FLOWS OKIHIRO SAWADA	398
A PRIORI ESTIMATES FOR THE EULER EQUATION WITH A FREE BOUNDARY BEN SCHWEIZER	401
Hyperbolic dynamics and beyond (Org.: M. Viana and V. Araujo)
ON THE CONTINUITY OF ENTROPY FOR NON-UNIFORMLY EXPANDING MAPS JOSÉ F. ALVES, KRERLEY OLIVEIRA and ALI TAHZIBI	409
INTEGRABILITY VERSUS FREQUENCY OF HYPERBOLIC TIMES AND THE EXISTENCE OF A.C.I.M. VíTOR ARAÚJO	415
MINIMAL ATTRACTORS YU. ILYASHENKO	421
GEODESIC PARAMETRIZATION OF GLOBAL INVARIANT MANIFOLDS OR WHAT DOES THE EQUADIFF 2003 POSTER SHOW? B. KRAUSKOPF and H.M. OSINGA	429
A POSSIBLE NEW FAMILY OF TWO DIMENSIONAL STRANGE ATTRACTORS ANTONIO PUMARIÑO and JOAN CARLES TATJER	434
C¹ GENERIC PESIN'S ENTROPY FORMULA ALI TAHZIBI	440
Symmetry and mechanics (Org.: M. Golubitsky, M. Roberts and A. Vanderbauwhede)
SWITCHING ALONG A NETWORK M. A. D. AGUIAR, B. S. D. CASTRO and I. S. LABOURIAU	449
BIPEDAL LOCOMOTION MARTIN GOLUBITSKY and CARLA ALVES-PINTO	452
INTRINSIC COMPLETE TRANSVERSALS AND THE RECOGNITION OF EQUIVARIANT BIFURCATIONS S. B. S. D. CASTRO and A. A. DU PLESSIS	458
STABILITY AND BIFURCATION BEHAVIOR OF THE FIGURE EIGHT SOLUTION OF THE THREE BODY PROBLEM JORGE GALÁN-VIOQUE, F. J. MUÑOZ-ALMARAZ and E. FREIRE	464
ON THE GROUP-INVARIANT SOLUTIONS OF THE GAS DYNAMICS EQUATIONS S. V. GOLOVIN	470
VIBRATING PLATES WITH CONCENTRATED MASSES AND VERY SMALL THICKNESS: LOW FREQUENCIES D. GÓMEZ, M. LOBO and E. PÉREZ	473
ON NON–DEGENERATE HAMILTONIAN HOPF BIFURCATIONS IN 3DOF SYSTEMS H. HANßMANN and J. C. VAN DER MEER	476
RELATIVE PERIODIC ORBITS OF SYMMETRIC LAGRANGIAN SYSTEMS C. MCCORD, J. MONTALDI, M. ROBERTS and L. SBANO	482
COMPLETE SYNCHRONIZATION OF SYMMETRICALLY COUPLED AUTONOMOUS SYSTEMS S. YANCHUK and K. R. SCHNEIDER	494
Shock waves and conservation laws(Org.: K. Zumbrun and D. Serre)
FROM KINETIC EQUATIONS TO MULTIDIMENSIONAL ISENTROPIC GAS DYNAMICS F. BERTHELIN and A. VASSEUR	499
STABILITY OF COMPRESSIBLE VORTEX SHEETS J.-F. COULOMBEL and P. SECCHI	502
SINGULARITIES OF THE SOLUTION OF THE INFINITE-DIMENSIONAL HYPERBOLIC SMOLUCHOWSKI SYSTEM DESCRIBING COAGULATION PROCESS V. A. GALKIN	505
EXISTENCE OF ROLLWAVES IN A VISCOUS SHALLOW WATER EQUATION J. HÄRTERICH	511
STABILITY OF DETONATION WAVES GREGORY LYNG, KEVIN ZUMBRUN and HELGE KRISTIAN JENSSEN	517
STABILITY OF LARGE EKMAN-HARTMANN BOUNDARY LAYERS F. ROUSSET	520
Nonlinear elliptic partial differential equations (Org.: A. Ambrosetti and C. Stuart)
ON THE DIRICHLET PROBLEM FOR H-SYSTEMS ON THE DISC WITH PRESCRIBED MEAN CURVATURE PAOLO CALDIROLI and ROBERTA MUSINA	525
PERMANENCE AND SEGREGATION OF SPECIES FOR LARGE INTERACTIONS IN HETEROGENEOUS ENVIRONMENT S. CANO-CASANOVA and J. LÓPEZ-GÓMEZ	531
ON MORSE THEORY FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS INVOLVING P - LAPLACE OPERATOR S. CINGOLANI	534
SOME RESULTS FOR ELLIPTIC EIGENVALUE PROBLEMS WITH MOVING MIXED BOUNDARY CONDITIONS E. COLORADO and I. PERAL	540
BIFURCATIONS IN DEGENERATE ELLIPTIC EQUATIONS R. LAISTER and R. E. BEARDMORE	546
POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS WITH CRITICAL LOWER ORDER TERMS VITALI LISKEVICH, SOFYA LYAKHOVA and VITALY MOROZ	549
A VARIATIONAL APPROACH TO SELF-SIMILAR SOLUTIONS FOR SEMILINEAR HEAT EQUATIONS YŪKI NAITO	555
MULTIPLE POSITIVE SOLUTIONS FOR THE BREZIS-NIRENBERG PROBLEM ON THE SPHERE $\mathbb{S}^N$ S. STINGELIN	558
MINIMAX METHOD, INVARIANT SETS, AND APPLICATIONS TO NODAL SOLUTIONS OF NONLINEAR ELLIPTIC PROBLEMS ZHI-QIANG WANG	561
Algebraic aspects and optimisation in dynamical systems (Org.: O.J. Vrieze, R.L.M. Peeters and H.Th. Jongen)
OPTIMAL CONTROL OF SYSTEMS WITH PERIODIC AND DIRICHLET BOUNDARY CONDITIONS M. BARTKIEWICZ and S. WALCZAK	569
ON THE RIEMANNIAN MANIFOLD STRUCTURE OF CLASSES OF LINEAR SYSTEMS R. L. M. PEETERS and B. HANZON	575
IDENTIFIABILITY OF HOMOGENEOUS POLYNOMIAL SYSTEMS USING THE STATE ISOMORPHISM APPROACH R. L. M. PEETERS and B. HANZON	581
BALANCED STATE REPRESENTATIONS FROM HIGHER-ORDER MODELS JAN C. WILLEMS and PAOLO RAPISARDA	587
Case studies in theoretical interpretation of numerical experiments (C. Simó and H. Broer)
EXISTENCE AND MEASURE OF 2-QUASIPERIODICITY IN HAMILTONIAN ONE-AND-A-HALF DEGREE OF FREEDOM SYSTEMS H. W. BROER, M. VAN NOORT and C. SIMÓ	595
QUASI-PERIODIC HÉNON-LIKE ATTRACTORS IN THE LORENZ-84 CLIMATE MODEL WITH SEASONAL FORCING H. W. BROER, R. VITOLO and C. SIMÓ	601
SUDDEN TRANSITIONS TO CHAOS IN A SEMICONDUCTOR LASER WITH OPTICAL DELAY K. GREEN and B. KRAUSKOPF	607
NONLOCAL ONSET OF INSTABILITY IN AN ASSET PRICING MODEL WITH HETEROGENEOUS AGENTS A. GAUNERSDORFER, C.H. HOMMES and F.O.O. WAGENER	613
ON THE FRACTALIZATION OF INVARIANT CURVES ÀNGEL JORBA and JOAN CARLES TATJER	619
CONTINUATION OF PERIODIC ORBITS IN LARGE-SCALE DISSIPATIVE SYSTEMS J. SÁNCHEZ, M. NET, B. GARCíA-ARCHILLA and C. SIMÓ	625
ON THE USE OF LYAPUNOV EXPONENTS TO DETECT GLOBAL PROPERTIES OF THE DYNAMICS CARLES SIMÓ	631
Infinite-dimensional dynamics (Org.: B. Fiedler and G. Raugel)
A REGULARIZED PERONA-MALIK FUNCTIONAL: SOME ASPECTS OF THE GRADIENT DYNAMICS G. BELLETTINI and G. FUSCO	639
LONG-TIME DYNAMICS OF REACTION-DIFFUSION EQUATIONS ON THIN TWO-LAYER DOMAINS I. D. CHUESHOV and A. M. REKALO	645
SPIRAL WAVE MOTION IN REACTION-DIFFUSION SYSTEMS M. GEORGI and N. JANGLE	651
KRAWCZYK METHOD FOR PROVING THE EXISTENCE OF PERIODIC ORBITS OF INFINITE DIMENSIONAL DISCRETE DYNAMICAL SYSTEMS Z. GALIAS	657
CONVERGENCE OF SOLUTIONS OF A NON-LOCAL PHASE-FIELD SYSTEM WITH MEMORY H. PETZELTOVÁ	663
WEAKLY NONLINEAR LONG-TIME BEHAVIOR OF SOLUTIONS TO A HYPERBOLIC RELAXATION SYSTEMS R. ORIVE	666
TRANSVERSALITY IN SEMILINEAR PARABOLIC EQUATIONS ON THE CIRCLE CARLOS ROCHA	672
THE CONCEPT OF ADJACENCY FOR STATIONARY AND NON-STATIONARY SOLUTIONS OF SCALAR SEMILINEAR PARABOLIC PDE M. WOLFRUM	678
Quasiperiodicity (Org.: H. Hanßmann and H. Broer)
INTEGRABLE ELLIPSOIDAL BILLIARDS WITH SEPARABLE POLYNOMIAL POTENTIALS S. ABENDA and YU. FEDOROV	687
DYNAMICS AND DIGITS: ON THE UBIQUITY OF BENFORD'S LAW A. BERGER	693
A HAMILTONIAN KAM THEOREM FOR BUNDLES OF LAGRANGEAN TORI H. W. BROER, R. H. CUSHMAN and F. FASSÒ	696
QUASI–PERIODIC RESPONSE SOLUTIONS AT NORMAL–INTERNAL RESONANCES HENK BROER, HEINZ HANßMANN, ÀNGEL JORBA, JORDI VILLANUEVA and FLORIAN WAGENER	702
NORMAL LINEAR STABILITY OF QUASI-PERIODIC TORI IN THE HAMILTONIAN 1 : -1 RESONANCE CASE H. W. BROER, J. HOO and V. NAUDOT	708
EXTENSION OF CATASTROPHE THEORY TO DULAC UNFOLDINGS H. W. BROER, V. NAUDOT and R. ROUSSARIE	714
PERSISTENCE OF QUASI PERIODIC ORBITS IN FAMILIES OF REVERSIBLE SYSTEMS WITH A 1:1 RESONANCE M.C. CIOCCI	720
AVERAGING FOR QUASIPERIODIC SYSTEMS H. SCOTT DUMAS and JAMES A. ELLISON	726
HAMILTONIAN BIFURCATIONS OF INVARIANT TORI WITH A VANISHING FLOQUET EXPONENT Heinz Hanßmann	732
THE MECHANISM OF PARABOLIC RESONANCE ORBITS ANNA LITVAK-HINENZON	738
Delay equations (J. Mallet-Paret and H.O. Walther)
ON THE STABILITY OF STATIONARY SOLUTIONS OF STOCHASTIC EVOLUTION EQUATIONS WITH DELAYS T. CARABALLO, M.J. GARRIDO-ATIENZA and B. SCHMALFUSS	747
HOW SMALL CAN A "SMALL SOLUTION" BE? G. DERFEL	750
MODELLING NONLINEAR OPTICS PHENOMENA USING DELAY DIFFERENTIAL EQUATIONS T. ERNEUX, L. LARGER, K. GREEN and D. ROOSE	756
APPROXIMATION OF THE CHARACTERISTIC ROOTS OF INTEGRAL EQUATIONS WITH DISTRIBUTED DELAYS T. LUZYANINA and D. ROOSE	762
DYNAMICS OF AN INVERTED PENDULUM SUBJECT TO DELAYED CONTROL J. SIEBER and B. KRAUSKOPF	768
Wave stability and pattern formation (Org.: A. Doelman and B. Sandstede)
SPIRAL INSTABILITIES IN PERIODICALLY FORCED EXTENDED OSCILLATORY MEDIA L. BRUSCH, H. K. PARK, M. BÄR and A. TORCINI	777
EDGE BIFURCATIONS IN SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS: A CASE STUDY A. DOELMAN, D. IRON and Y. NISHIURA	783
PROPAGATION PHENOMENA FOR KPP-TYPE EQUATIONS IN UNBOUNDED DOMAINS F. HAMEL	789
THE EFFECTS OF CONVECTIVE PROCESSES ON FRONT PROPAGATION IN VARIOUS REACTION-DIFFUSION EQUATIONS LUISA MALAGUTI, CRISTINA MARCELLI and SERENA MATUCCI	795
STATIONARY LOCALIZED SOLUTIONS, FRONTS, AND TRAVELING FRONTS TO THE GENERALIZED 1D SWIFT-HOHENBERG EQUATION L. M. LERMAN and L. A. BELYAKOV	801
SEMIFLUXONS IN A LONG JOSEPHSON JUNCTION WITH A π-DISCONTINUITY POINT HADI SUSANTO and STEPHAN A. VAN GILS	807
EXISTENCE AND STABILITY OF MULTIPLE SPOT SOLUTIONS FOR THE GRAY-SCOTT MODEL IN R² JUNCHENG WEI and MATTHIAS WINTER	813
Nonautonomous dynamics (Org.: R. Johnson, R. Obaya, G. Sell and Y. Yi)
SHARKOVSKII'S THEOREM AND DIFFERENTIAL EQUATIONS J. ANDRES	821
ASYMPTOTIC BEHAVIOUR AND ATTRACTORS OF 2D-NAVIER-STOKES MODELS WITH DELAYS T. CARABALLO and J. REAL	827
INVARIANT MANIFOLDS, GLOBAL ATTRACTORS AND ALMOST PERIODIC SOLUTIONS OF NON-AUTONOMOUS DIFFERENCE EQUATIONS DAVID CHEBAN and CRISTIANA MAMMANA	833
ON A SADDLE-NODE BIFURCATION IN A PROBLEM OF QUASI-PERIODIC HARMONIC FORCING R. FABBRI and R. JOHNSON	839
UNIFORM COMPLETE GUIDING SETS FOR FINITE-DELAY DIFFERENTIAL EQUATIONS CARMEN NÚÑEZ and RAFAEL OBAYA	848
THE SPECTRUM OF SCHRÖDINGER OPERATORS WITH QUASI-PERIODIC POTENTIAL: A DYNAMICAL APPROACH JOAQUIM PUIG and CARLES SIMÓ	856
Normal forms and invariant manifolds (Org.: P. Bonckaert and F. Verhulst)
INVARIANT MANIFOLDS OF NEAR ROTATION MAPS PATRICK BONCKAERT and ERNEST FONTICH	865
CHAOTIC LASERS: MANIFOLDS, BIFURCATIONS AND SYMBOLIC DYNAMICS PIETER COLLINS and BERND KRAUSKOPF	871
NON-RESONANT INVARIANT MANIFOLDS IN NON-UNIFORMLY HYPERBOLIC SYSTEMS ERNEST FONTICH, RAFAEL DE LA LLAVE and PAU MARTÍN	877
RESONANCES AND SUBHARMONIC BIFURCATIONS OF LARGE AMPLITUDE PERIODIC ORBITS OF PLANAR POLYNOMIAL VECTOR FIELDS MARCELO MESSIAS	880
Singular perturbations (Org.: T. Kaper, S. Szmolyan and F. Dumortier)
SLOW MANIFOLDS IN A SINGULARLY PERTURBED HAMILTONIAN SYSTEM V. GELFREICH and L.M. LERMAN	889
DYNAMICS ON DIFFERENT TIME SCALES IN THE YAMADA MODEL A. HUBER	895
CANARD SOLUTIONS AT NONGENERIC TURNING POINTS P. DE MAESSCHALCK and F. DUMORTIER	898
ON ACCURACY OF THE AVERAGING METHOD IN TWO-FREQUENCY SYSTEMS WITH SMALL HAMILTONIAN AND MUCH SMALLER NON-HAMILTONIAN PERTURBATIONS A. I. NEISHTADT	904
CONLEY INDEX THEORY FOR SLOW-FAST SYSTEMS: MULTI-DIMENSIONAL SLOW MANIFOLD HIROE OKA	910
A GEOMETRIC ANALYSIS OF THE LAGERSTROM MODEL: EXISTENCE OF SOLUTIONS AND RIGOROUS ASYMPTOTIC EXPANSIONS NIKOLA POPOVIĆ	916
EXISTENCE OF A SLOW INVARIANT MANIFOLD FOR A CLASS OF RANDOM DIFFERENTIAL EQUATIONS WITH TWO TIME SCALES B. SCHMALFUSS and K. R. SCHNEIDER	919
LOSS OF STABILITY SCENARIO IN THE ZIEGLER SYSTEM E.V. SHCHETININA	922
POINCARÉ MAPS FOR RELAXATION OSCILLATIONS IN ℝ³ - INVARIANT MANIFOLDS, CANARDS AND TURNING POINTS MARTIN WECHSELBERGER	925
CANARDS AND HORSESHOES IN THE FORCED VAN DER POL EQUATION WARREN WECKESSER	931
Differential geometric foliations and flows (Org.: J. Sotomayor)
PRINCIPAL MEAN CURVATURE FOLIATIONS ON SURFACES IMMERSED IN ℝ⁴ R. GARCIA, L. F. MELLO and J. SOTOMAYOR	939
LINE FIELDS ON SURFACES IMMERSED IN ℝ⁴ L. F. MELLO	951
THE NATURE OF ELLIPTIC SECTORS IN THE PRINCIPAL FOLIATIONS OF SURFACE THEORY BRIAN SMYTH	957
Homoclinic and heteroclinic dynamics (Org.: H. Kokubo and A.J. Homburg)
BELLOWS BIFURCATING FROM DEGENERATE HOMOCLINIC ORBITS IN CONSERVATIVE SYSTEMS A.J. HOMBURG and J. KNOBLOCH	963
TOPOLOGICAL CLASSIFICATION FOR MULTIPLE SADDLE-CONNECTIONS CLEMENTA ALONSO GONZÁLEZ	972
SHIL'NIKOV HOMOCLINIC ORBITS IN THE UNFOLDING OF A CODIMENSION-3 SINGULARITY S. IBÁÑEZ and J. A. RODRÍGUEZ	975
THE REVERSIBLE HOMOCLINIC PITCHFORK BIFURCATION REVISITED T. WAGENKNECHT	978
DETECTION OF HOMOCLINIC AND HETEROCLINIC BEHAVIOR IN HAMILTONIAN SYSTEMS WITH SADDLE-CENTERS K. YAGASAKI	984
Mathematical aspects of celestical mechanics (Org.: A. Albouy and R. Moeckell)
CO-CIRCULAR CENTRAL CONFIGURATIONS IN THE FOUR-BODY PROBLEM MARSHALL HAMPTON	993
N-BODY CHOREOGRAPHIES WITH A REFLECTIONAL SYMMETRY - COMPUTER ASSISTED EXISTENCE PROOFS TOMASZ KAPELA	999
STABILITY OF HOMOGRAPHIC SOLUTIONS OF THE PLANAR THREE-BODY PROBLEM WITH HOMOGENEOUS POTENTIALS REGINA MARTÍNEZ, ANNA SAMÀ and CARLES SIMÓ	1005
SYMMETRIC PERIODIC ORBITS IN THE ISOSCELES THREE BODY PROBLEM DANIEL OFFIN and JÉROME GRAND'MAISON	1011
Contributed talks
NEW SOBOLEV EQUATIONS AND DYNAMICAL POTENTIALS A. B. ALSHIN, M. O. KORPUSOV, YU. D. PLETNER and A.G. SVESHNIKOV	1021
APPLICATION OF QUASI-UNIFORM GRIDS FOR NUMERICAL SOLUTION OF INITIAL-BOUNDARY VALUE PROBLEMS IN UNBOUNDED DOMAIN A.B. ALSHIN, E.A. ALSHINA and N.N. KALITKIN	1024
STABILITY OF COUPLED DELAY DIFFERENTIAL EQUATIONS NEAR HOPF BIFURCATION FATIHCAN M. ATAY	1027
PROPERTIES OF 2D NAVIER-STOKES FLOW IN INFINITE STRIP FOR SPATIALLY NON-DECAYING INITIAL DATA A. AFENDIKOV	1030
PERTURBED FREDHOLM BVP'S FOR DELAY DIFFERENTIAL SYSTEMS A. BOICHUK	1033
CUBIC POLYNOMIALS ON SO(3) M. CAMARINHA and L. ABRUNHEIRO	1036
ON A PROBLEM OF HARTMAN-WINTNER FOR DIFFERENCE EQUATIONS N. CHERNYAVSKAYA and L. SHUSTER	1039
ATTRACTORS OF DELAYED DIFFERENTIAL EQUATIONS WITHOUT UNIQUENESS T. CARABALLO, P. MARÍN-RUBIO and J. VALERO	1042
UNSTABLE MANIFOLDS COMPUTATION FOR THE TWO-DIMENSIONAL PLANE POISEUILLE FLOW PABLO S. CASAS and ÀNGEL JORBA	1045
SOME QUALITATIVE PROPERTIES OF SOLUTIONS TO NONCONVEX HYPERBOLIC DIFFERENTIAL INCLUSIONS AURELIAN CERNEA	1048
REMARKS ON BIFURCATION IN ELLIPTIC BOUNDARY VALUE PROBLEMS YUANJI CHENG and LINA WANG	1051
ON A PARABOLIC PROBLEM WITH DIFFUSION ON THE BOUNDARY ARISING IN CLIMATOLOGY J. I. DIAZ and L. TELLO	1056
ON STABILITY OF NONAUTONOMOUS INTEGRO-DIFFERENTIAL EQUATIONS ALEXANDER DOMOSHNITSKY	1059
STABILITY OF CLASSES OF SOLUTIONS TO PARTIAL DIFFERENTIAL RELATIONS CONSTRUCTED BY QUASICONVEX FUNCTIONS AND NULL LAGRANGIANS A. A. EGOROV	1065
STABILITY OF EQUILIBRIA OF A NON-LINEAR POPULATION DYNAMICAL MODEL J.Z. FARKAS	1068
GLOBAL ANALYSIS OF A CANONICAL CUBIC SYSTEM V. A. GAIKO and W. T. VAN HORSSEN	1071
ON ℒ^P-STABILITY OF NUMERICAL SCHEMES FOR LINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS HAGEN GILSING	1074
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE ZAKHAROV SYSTEM M. GUZMÁN-GÓMEZ	1080
REVIEW OF MATHEMATICAL MODELLING IN THE STUDY OF COLLECTIVE MOVEMENT OF DICTYOSTELIUM DISCOIDEUM S.C. HILLE	1083
CONSTRAINED MOUNTAIN PASS ALGORITHM JIŘÍ HORÁK	1086
FORWARD-BACKWARD PARABOLIC EQUATIONS AND THEIR TIME DELAY APPROXIMATIONS D. HORSTMANN	1089
VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY F. IZSÁK	1092
DETERMINING FUNCTIONALS FOR BIFURCATIONS ON A FINITE-TIME INTERVAL IN VARIATIONAL INEQUALITIES H. KANTZ and V. REITMANN	1098
APPROXIMATIONS OF THE EQUATIONS DESCRIBING MOTIONS OF BINGHAM FLUIDS N. A. KARAZEEVA	1101
SINGULAR PROBLEMS FOR SELF-SIMILAR SOLUTIONS TO THE SYSTEMS OF NONLINEAR WAVE EQUATIONS IN THE INFLATIONARY COSMOLOGY N. B. KONYUKHOVA, A. L. DYSHKO and N. A. VORONOV	1105
QUENCHING OF AEROELASTIC OSCILLATIONS OF A SEESAW OSCILLATOR BY MEANS OF A DYNAMIC ABSORBER H. LUMBANTOBING and T. I. HAAKER	1108
STABILITY AND LINEAR CHAIN TRICK JOSÉ J. MIGUEL, ANDREI SHINDIAPIN and ARCADY PONOSOV	1111
A VECTOR FIELD MODEL OF A SADDLE-NODE HOPF BIFURCATION WITH GLOBAL REINJECTION BART OLDEMAN and BERND KRAUSKOPF	1114
HYPERBOLICITY TEST AND STRUCTURAL STABILITY G. S. OSIPENKO	1117
GLOBAL EXISTENCE, BLOW UP AND ASYMPTOTIC RESULTS FOR KIRCHHOFF STRINGS ON ℝ^N PERIKLES G. PAPADOPOULOS and NIKOS M. STAVRAKAKIS	1122
ON STABILITY OF STOCHASTIC NONLINEAR NON-AUTONOMOUS SYSTEMS WITH DELAY A. RODKINA	1125
PHASE TRANSITIONS AND ASPECTS OF HEAT PROPAGATION IN LOW TEMPERATURE SOLIDS KATARZYNA SAXTON and RALPH SAXTON	1128
EXISTENCE AND STRUCTURE OF SINGULAR SOLUTIONS FOR $\Delta U = (U - C)_+^P$, P > 1 IN ℝ^N, N > 2; C > 0. TADIE	1131
LOWER BOUNDS FOR LARGE SOLUTIONS OF SOME ANISOTROPIC PROBLEMS IN REGULAR BOUNDED DOMAINS TADIE	1134
OPTIMIZING IMPROVED HARDY INEQUALITIES FOR THE BIHARMONIC OPERATOR A. TERTIKAS and N. B. ZOGRAPHOPOULOS	1137
EXISTENCE OF POSITIVE DECAYING SOLUTIONS OF SINGULAR QUASILINEAR ORDINARY DIFFERENTIAL EQUATIONS HIROYUKI USAMI	1140
ON ASYMPTOTICS FOR WEAKLY NONLINEAR WAVE, BEAM, AND PLATE EQUATIONS W.T. VAN HORSSEN	1143
ON ASYMPTOTIC APPROXIMATIONS OF FIRST INTEGRALS FOR A STRONGLY NONLINEAR FORCED OSCILLATOR S. B. WALUYA and W.T. VAN HORSSEN	1146
CLASSES OF FUNCTIONS FULFILLING SECOND ORDER HARDY TYPE INTEGRAL INEQUALITIES ON THE EXAMPLE OF 'STANDARD' HARDY INEQUALITY KATARZYNA WOJTECZEK	1149
ON THE VIBRATIONS OF A SIMPLY SUPPORTED SQUARE PLATE ON A WEAKLY NONLINEAR ELASTIC FOUNDATION M.A. ZARUBINSKAYA and W.T. VAN HORSSEN	1152
BACK MATTER	1155
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