# 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)

__Plenarys__

**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 C ^{k }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), ***C ^{1 }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.), ***C ^{1}–*

*W-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 Z_{2 }-equivariant vector fields in R^{3 }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 C^{1} 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 C^{2}*

** ****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 R^{3}*

** ****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 C^{2}*

** ****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/**w**z ^{d}*

** ****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*