Invariant measures for interval maps with critical points and singularities (2008)
Araujo, Vitor, Luzzatto, Stefano, Viana, Marcelo
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with...
Hyperbolic Dynamical Systems (2008)
The theory of uniformly hyperbolic dynamical systems was initiated in the 1960's (though its roots stretch far back into the 19th century) by S. Smale, his students and collaborators, in the west,...
Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps (2008)
Varandas, Paulo, Viana, Marcelo
We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Holder continuous potentials with not very...
Towards a Theory of Chaotic Dynamics (2007)
44> j+1 = f(x j ) is the trajectory of the initial state x 0 . If the transformation f is invertible, then we also have a backward trajectory : : : x 2 ; x 1 ; x 0 dened by x j+1 = f(x j )....
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices (2007)
Christian Bonatti, Marcelo Viana
We propose a geometric sucient criterium \a la Furstenberg " for the existence of non-zero Lyapunov exponents for certain linear cocycles over hyperbolic transformations: non-existence of...
Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices (2007)
Christian Bonatti, Xavier Gómez-mont, Marcelo Viana
We propose a geometric sufficient criterium “à la Furstenberg ” for the existence of non-zero Lyapunov exponents for certain linear cocycles over hyperbolic transformations: non-existence of...
Pisa Lectures on Lyapunov Exponents (2007)
These notes cover the course we taught at the research trimester on Dynamical Systems organized by Stefano Marmi at the Centro di Ricerca Matematica Ennio di Giorgi/Scuola Normale Superiore di Pisa...
Simplicity of Lyapunov spectra: a sufficient criterion (2006)
We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h-Raugi and Gol'dsheid-Margulis,...
Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms (2006)
Oliveira, Krerley, Viana, Marcelo
We prove existence of maximal entropy measures for an open set of non-uniformly expanding local diffeomorphisms on a compact Riemannian manifold. In this context the topological entropy coincides...
Ergodic theory of interval exchange maps (2006)
A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichm¿uller flows, starting from...
Singular-hyperbolic attractors are chaotic (2005)
Araujo, Vitor, Pacifico, Maria Jose, Pujals, Enrique, Viana, Marcelo
We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly...
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture (2005)
We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichm\"uller flow on (any connected component of a stratum of) the moduli space of Abelian differentials on...
The Lyapunov exponents of generic volume-preserving and symplectic maps (2005)
We show that the integrated Lyapunov exponents of $C^1$ volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is...
Bonatti, C. (Christian), Díaz, Lorenzo J, Viana, Marcelo
Incluye bibliografía e índice
The Lyapunov exponents of generic volume preserving and symplectic systems (2005)
We show that the integrated Lyapunov exponents of C1 volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial...
Abstract. We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller flow on (any connected component of a stratum of) the moduli space of Abelian...
Parameter exclusions in Henon-like systems (2003)
Luzzatto, Stefano, Viana, Marcelo
This survey is a presentation of the arguments in the proof that Henon-like maps f_a(x,y)=(1-a x^2,0) + R(a,x,y) with |R(a,x,y)|< b have a "strange attractor", with positive Lebesgue probability in...
Abundance of Stable Ergodicity (2003)
Christian Bonatti, Carlos Matheus, Marcelo Viana, Amie Wilkinson
We consider the set PH! (M) of volume preserving partially hyperbolic dieomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even...
Are most dynamical systems hyperbolic ? (2002)
ICM2002 Satellite Conference: New Directions in Dynamical Systems Abstracts (August 2002 Kyoto)
Are most dynamical systems hyperbolic ? (2002)
ICM2002 Satellite Conference: New Directions in Dynamical Systems Abstracts (August 2002 Kyoto)
The Lyapunov exponents of generic volume preserving and symplectic systems (2002)
We show that the integrated Lyapunov exponents of $C^1$ volume preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is...
Non-periodic bifurcations at the boundary of hyperbolic systems / (2001)
Sabini, Paulo Rogério., Viana, Marcelo.
Instituto de Matemática Pura e Aplicada.
Expoente de Lyapunov nulos em sistemas conservativos / (2001)
Bochi, Jairo Da Silva., Viana, Marcelo.
Instituto de Matemática Pura e Aplicada.
Statistical stability for robust classes of maps with non-uniform expansion (2000)
Alves, Jose F., Viana, Marcelo
We consider open sets of maps in a manifold $M$ exhibiting non-uniform expanding behaviour in some domain $S\subset M$. Assuming that there is a forward invariant region containing $S$ where each map...
Positive Lyapunov exponents - for Lorenz-like families with criticalities (2000)
Luzzatto, Stefano, Viana, Marcelo
We introduce a class of one-parameter families of real maps extending the classical geometric Lorenz models. These families combine singular dynamics (discontinuities with infinite derivative) with...
Hausdor dimension of non-hyperbolic repellers II: DA dieomorphisms (2000)
This is the rst paper in a two-part series devoted to studying the Hausdor dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that...
Hausdor dimension of non-hyperbolic repellers II: DA dieomorphisms (2000)
This is the rst paper in a two-part series devoted to studying the Hausdor dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that...
Statistical Stability for Robust Classes of Maps With Non-Uniform Expansion (2000)
We consider open sets of transformations in a manifold M , exhibiting nonuniformly expanding behaviour in some forward invariant domain U M . Assuming that each transformation has a unique SRB...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms - the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
Jos'e Alves Christian, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (2000)
Jose F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of di#eomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
Hausdorff dimension of non-hyperbolic Repellers derived from Anosov diffeomorphisms / (1999)
Horita, Vanderlei M., Viana, Marcelo.
Instituto de Matemática Pura e Aplicada.
We consider open sets of maps in a manifold M exhibiting non-uniform expanding behaviour in some domain S M. Assuming that there is a forward invariant region containing S where each map has a unique...
Statistical Stability for Robust Classes of Maps With Non-Uniform Expansion (1999)
Jos Alves And, Jose F. Alves, Marcelo Viana
We consider open sets of transformations in a manifold M , exhibiting nonuniformly expanding behaviour in some forward invariant domain U M . Assuming that each transformation has a unique SRB...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti And, Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E uu (uniformly expanding) and a subbundle E c , dominated by E uu . We...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E uu (uniformly expanding) and a subbundle E c , dominated by E uu . We...
SRB measures for partially hyperbolic systems whose central direction is mostly expanding (1999)
José F. Alves, Christian Bonatti, Marcelo Viana
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly...
SRB measures for partially hyperbolic systems whose central direction is mostly contracting (1999)
Christian Bonatti, Marcelo Viana, Dominated E
We consider partially hyperbolic dieomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E (uniformly expanding) and a subbundle E , dominated by E .
Attractors and time averages for Random maps / (1998)
Instituto de Matemática Pura e Aplicada.
Castro Jr., Augusto A., Viana, Marcelo.
Instituto de Matemática Pura e Aplicada.
Rios, Isabel L., Viana, Marcelo.
Instituto de Matemática Pura e Aplicada.
Dynamics: A Probabilistic and Geometric Perspective (1998)
. An overview of recent developments and open questions aiming at a global theory of general (non-conservative) dynamical systems. 1991 Mathematics Subject Classification: 58, 34, 60 Keywords and...
Dynamics: A Probabilistic and Geometric Perspective (1998)
An overview of recent developments and open questions aiming at a global theory of general (non-conservative) dynamical systems.
Global strange attractors after collision of horseshoes with periodic sinks / (1998)
Instituto de Matemática Pura e Aplicada.
The Statistics of Attractors (1996)
64> 0:363961; 0:091883; 0:275649; 0:826948; 0:480843; 0:442530; 0:327591; 0:982774; 0:948322; 0:844967; 0:534901; 0:604702; 0:814105; 0:442315; 0:326945; 0:980836; 0:942508; 0:827525; 0:482574;...
Strong Stochastic Stability and Rate of Mixing for Unimodal Maps (1994)
. We consider small random perturbations of a large class of nonuniformly hyperbolic unimodal maps and prove stochastic stability in the strong sense (L 1 -convergence of invariant densities) and...
Multidimensional Nonhyperbolic Attractors
We construct smooth transformations and diffeomorphisms exhibiting nonuniformly hyperbolic attractors with multidimensional sensitiveness on initial conditions: typical orbits in the basin of...
Dynamical Systems: Moving into the Next Century
ability of the Solar system, that was the initial motivation. Kolmogorov, Arnold, Moser theory remained, to present days, one of the most active areas in Dynamical Systems, through major...