6 papers
Invariance principle in dynamical systems
Karina Marin, Mauricio Poletti
In this survey we talk about what is known as Invariance Principle in dynamical systems. It states that the disintegration of measures with zero center Lyapunov exponents admits so…
Measures of maximal entropy for non-uniformly hyperbolic maps
Yuri Lima, Davi Obata, Mauricio Poletti
For maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbol…
Uniqueness of the measure of maximal entropy for geodesic flows on surfaces
Yuri Lima, Davi Obata, Mauricio Poletti
We prove that if a geodesic flow on a closed orientable surface is transitive and has positive topological entropy, then it has a unique measure of maximal entropy. This…
Exponential mixing of measures of maximal entropy for certain skew products
Karina Marin, Mauricio Poletti, Filiphe Veiga
We establish a relation between the continuity of the fiber entropy and the continuity of the fiber Lyapunov exponents for skew products with 2-dimensional fibers. This result exte…
Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms
Karina Marin, Davi Obata, Mauricio Poletti
We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is -a…
Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy
Juan Carlos Mongez, Maria José Pacifico, Mauricio Poletti
We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensiona…