4th Quadriennal International Conference on Dynamical Systems

Brief History and Main Topics

International meetings on Dynamical Systems have been organized at IMPA, on a quadriennal  basis,  since 1981. These meetings are attended by a  large number of the most distinguished experts in this area and cover several active domains of Dynamics. 

The present meeting is devoted mainly to the following topics:

  • Fractal dimensions and homoclinic byfurcations;
  • Strange attractor and invariant measures;
  • Holomorphic dynamical systems;
  • Dynamics of endomorphisms of the interval or the circle;
  • Conservative dynamical systems and variational methods.

Scientific Committee

 John Mather (Princeton, USA)
Welington de Melo (IMPA, Brazil)
John Milnor (Stony Brook, USA)
Jurgen Moser (ETH, Switzerland)
Sheldon Newhouse (Michigan State, USA)
Robert Roussarie (Dijon, France)
Yakov. Sinai (Princeton, USA)
Marcelo Viana (IMPA, Brazil)
Jean Christophe Yoccoz (Collège de France)
Jacob Palis (IMPA, Brazil)

Scientific Program



Lyubich (SUNY, NY), Regular and stochastic dynamics in the real quadratic family

 C. Yoccoz (Collège de France), Modular aspects of the Brjuno function

 Ruelle (IHES), Nonequilibrium statistical mechanics and hyperbolic dynamics

 Herman (Univ. Paris VII), Existence of invariant circles and invariant tori for Hamiltonian systems with a torsion condition

 G. Moreira (IMPA), Cantor sets and dynamical spectra

 Kozlowski (Univ. of Amsterdam), Axiom A maps are dense in the space of Ck unimodal maps

 de Faria (IME/USP), Rigidity of critical circle mappings

 Pujals (UFRJ), Transitivity and partial hyperbolicity

 Markarian (Univ. Montevideo), Conditionally invariant measures for Anosov maps with small holes

 MacKay (Cambridge Univ.), Discrete breathers

 Shub (IBM, Watson, NY), Stable ergodicity and julienne quasi-conformality

 Viana (IMPA), Ergodic properties of partially hyperbolic systems

 Takens (Groningen Univ.), Application of methods of non-linear time series analysis to fluid bed data

 Sotomayor (IME/USP), Critical bifurcations of three dimensional vector fields with a first integral

 C. Zeeman (Oxford Univ.), Geometric unfolding of a difference equation

Szasz (Hungarian Ac.Sc), Ball avoiding theorems

 Milnor (SUNY, NY), Pasting together Julia sets (a mating example)

 Wagoner (Univ.Cal.Berkeley), The Kim-Roush counterexample to William’s conjecture

 Mather (Princeton Univ.), Variational construction of orbits

 Swiatek (Penn.St.Univ), Decay of geometry in the cubic family

 Roussarie (Univ. Dijon), Quasi-conformal mapping theorem and bifurcations

 Martens (SUNY, NY), Convergence of renormalization in interval dynamics(without complex dynamics)

Bolibruch (Steklov Institute), Isomonodromic confluence of Fuchsian singularities

 Neishtadt (Space Res. Inst., Russia), Jumps of adiabatic invariant at separatrix in volume-preserving systems

 Gutierrez (IMPA), Affine interval exchange transformations with wandering intervals

 Tresser (IBM, Watson, NY), On the geometry of master-slave synchronization

 J.Pacífico (UFRJ), C1 robust singular transitive sets for three-dimensional flows are either attractors or repellers

 Matsumoto, (Nihon Univ.), Signs of index one fixed points of area preserving homeomorphisms

 Hayashi (Waseda Univ.), C1W-stability, a connecting lemma, and a make or break lemma

 Eliasson (Royal Inst. Technology), Floquet solutions for the higher dimensional quasi-periodic Schrodinger equation

Oliva (Univ.Tec. Lisboa), Anosov flows induced by non integrable D-geodesic flows

 Yu Il’Yashenko (Moscow St. Univ.), Random dynamical systems (RDS) as subsystems of smooth ones

 Smillie (Univ. Cornell), The connectivity of two dimensional Julia sets

 Ledrappier (Ecole Polytechnique), Invariant measures for the stable foliation on abelian covers

 Pollicott (Univ. of Manchester), Counting closed orbits for hyperbolic flows

 Newhouse (Michigan St.Univ), Asymptotic measures for area decreasing maps of the plane


Parallels Sections

 F.Alves (IMPA/ Univ. of Porto), SRB measures for multidimensional nonhyperbolic attractors

 Dumortier (Limburgs Univ. Centrum), Nilpotent singularities of Z2 -equivariant vector fields in R3 and heteroclinic cycles

 Pinto (Univ. of Porto), Renormalization gives all surface Anosov diffeomorphisms with a smooth invariant measure

 Fisher (UFRGS), Self -similar return maps for some maps with an indifferent fixed point

 Simo (Univ. of Barcelona), Analytical estimates of parameters for which a saddle-node homoclinic tangency occurs in perturbations of area preserving maps

 Bamon (Univ. de Chile), A family of n-dimensional differential equations with Lorenz like attractors

 Luzzatto (Univ. of Warwick), Hyperbolicity and bounded recurrence in families of one-dimensional maps

 Iturriaga (CIMAT), Convex Hamiltonians without conjugate points

 Schmeling (Penn. State Univ.), On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture

 Diaz (PUC/RJ), Infinitely many sinks in the C1 topology

 Langevin (Univ. Dijon), Anosov-Smale diffeomorphisms in dimension 2

 Paternain (Fac. Ingenieria), On the regularity of the Anosov splitting for Euler-Lagrange flows

 Gutkin (Univ. Southern Cal.), Billiards in polygons and related topics

 Lopes de Medrano (UNAM), Construction of compact complex manifolds from dynamical systems

 Contreras (PUC/RJ), Globally minimizing orbits of autonomous lagrangians

 Buzzard (Indiana Univ.), Stability questions for automorphisms of C2

 Labarca (Univ. de Santiago de Chile), Topological classification of Lorenz maps on the interval

 Krikorian (École Polytechnique), Reducibility of linear quasi-periodic systems

 Broer (Groningen), Resonance tongues in Hill’s equations: a geometry approach

 Graczik (Michigan St. Univ.), Geometry of Siegel disks

 Burns (Northwestern Univ.), Stable ergodicity of skew-products

Weiss (Penn. State Univ.), Spheres with positive curvature and nearly dense orbits for the geodesic flow

Baladi (Univ. Geneva), The spectra of coupled map lattices

 Sands (SUNY), A simple proof of complex bounds

 Morales (UFRJ), A note on singular hyperbolic systems

Levin (Hebrew Univ.), The topology of the Julia set of real polynomials

 Baesens (Cambridge Univ.) Gradient dynamics of Frenkel-Kontorova models

 Bressaud (IME/USP), Transfer operators for subshifts on an infinite alphabet

 Khanin (Heriott-Watt Univ.), Minimizing orbits for random 1-d Lagrangians

 Aoki (Tokyo Met. Univ), Differentiable maps having hyperbolic sets

 Ishii (Univ. of Tokyo), A kneading theory for Lozi mappings: Admissibility, monotonicity and horseshoes

 Sambarino (IMPA), On a Palis’conjecture

 Garcia (UFGo), Structural stability of asymptotic lines of immersed surfaces on R3

 de La Llave (Univ. of Texas), Spectral properties of push-forward operators

Pugh (Univ. of Cal., Berkeley), Focal stability

 Kosygin (Princeton Univ), Examples of ergodic twist maps

 Nowicki (Warsaw Univ.), Non-uniform hyperbolicity and absolutely continuous invariant measures

 Robinson (Northwestern Univ.), Homoclinic bifurcation to a semi-orientable Lorenz attractor

 Mora (Int.Venez.Inv.Cient), Quasiperiodic bifurcations and homoclinic tangencies

 Bedford (Indiana Univ.), Dynamics of polynomial diffeormorphisms of C2

 Beguin (Univ. Bourgogne), Smale flows on 3-manifolds

Tsujii (Hokkaido Univ.), Some monotone families of piecewise linear unimodal maps

 Vieitez (Fac. Ingenieria),3D-expansive diffeomorphisms without wandering points

 Toom (IME/USP), Some growth mode

 de Carvalho (Univ. of Cal.,Berkeley), The dynamics of surface homeomorphisms and the pruning front conjecture

 Oka (Ryukoku Univ.) On the monotonicity of topological entropy for symmetric PL bimodal maps

 Bobenrieth (Univ. del Bio-Bio), On the dynamics of the rational maps Z ® 1+1/wzd

 Kokubu (Kyoto Univ.), Homoclinic doubling cascades in vector fields

 Sánchez-Morgado (UNAM), On the creation of conjugate points for Hamiltonian systems

Calvo (CIMAT), Foliations with a Kupka component of radial transversal type

 Massart (Univ. of Warwick), Differentiability of Mather’s b-function for Lagrangians on a surface

 Flexor (Univ. Paris-Sud), Fixed points of renormalization

 C. Tatjer (Univ. di Barcelona), Return maps near homoclinic tangencies in dimension 3

 J. D. Carneiro (UFMG), On the minimal action functions for Lagrangians associated to magnetic fields

 Sirvent (Univ. Simon Bolivar), Geodesic laminations as geometric realizations of Pisot substitutions

 C. Martín (Univ.Simon Bolivar), Hopf bifurcations and homoclinic tangencies

 I. Bogdanov (Moscow St. Univ.), Dynamical systems on the plane

 Shishikura (Univ. of Tokyo), Some applications of Yoccoz’ method on complex quadratic polynomials

Chernov (Univ. of Alabama, Birmingham), Statistical properties of piecewise hyperbolic systems in high dimensions