15 citations · 40 across the 16 of their papers we have counts for
20 papers
Entropy and semiconjugacy on surfaces
Pablo D. Carrasco, Federico Rodriguez Hertz, Jana Rodriguez Hertz +1
Let be a diffeomorphism in the isotopy class of a pseudo-Anosov homeomorphism such that and have the same topological entropy. In 1988, Handel proved tha…
Thermodynamic Formalism for Quasimorphisms: Lattices in Higher Rank Semisimple Lie Groups
Pablo D. Carrasco, Federico Rodriguez-Hertz
We give a new proof, based on thermodynamic formalism, of a foundational result of Burger and Monod in bounded cohomology. Let be a noncompact connected semisimple real Lie gro…
Thermodynamic formalism for Quasimorphisms: Bounded Cohomology and Statistics
Pablo D. Carrasco, Federico Rodriguez-Hertz
For a compact negatively curved space, we develop a thermodynamic formalism framework to study the space of quasimorphisms of its fundamental group modulo bounded functions. We pro…
On the Number of Periodic Points for Expansive Pseudo-Groups
Pablo D. Carrasco, Elias Rego, Jana Rodriguez-Hertz
In this work we consider foliations of compact manifolds whose holonomy pseudo-group is expansive, and analyze their number of compact leaves. Our main result is that in the codime…
Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations
Pablo D. Carrasco, Federico Rodriguez-Hertz
In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to Hölder potentials satisfy a strong rigidity property: they are de…
Non-uniformly hyperbolic endomorphisms
Martin Andersson, Pablo D. Carrasco, Radu Saghin
We show the existence of large open sets of area preserving endomorphisms of the two-torus which have no dominated splitting and are non-uniformly hyperbolic, meanin…
Geometrical constructions of equilibrium states
Pablo D. Carrasco, Federico Rodriguez-Hertz
In this note we report some advances in the study of thermodynamic formalism for a class of partially hyperbolic system -- center isometries, that includes regular elements in Anos…
Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map
Pablo D. Carrasco, Federico Rodriguez-Hertz
We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hö…
Equilibrium States for Center Isometries
Pablo D. Carrasco, Federico Rodriguez-Hertz
We develop a geometric method to establish existence and uniqueness of equilibrium states associated to some Hölder potentials for center isometries (as are regular elements of Ano…
Extended flexibility of Lyapunov exponents for Anosov diffeomorphisms
Pablo Carrasco, Radu Saghin
Bochi-Katok-Rodriguez Hertz proposed in [BKH21] a program on the flexibility of Lyapunov exponents for conservative Anosov diffeomorphisms, and obtained partial results in this dir…
A Symmetric Random Walk defined by the Time-One Map of a Geodesic Flow
Pablo D. Carrasco, Túlio Vales
In this note we consider a symmetric random walk defined by a Kalikow type system, where is the time-one map of the geodesic flow corresponding to an hyperbolic ma…
Invariance of entropy for maps isotopic to Anosov
Pablo D. Carrasco, Cristina Lizana, Enrique Pujals +1
We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of with simple central bundle (that is, when it decomposes…
A new example of robustly transitive diffeomorphism
Pablo D. Carrasco, Davi Obata
We present an example of a -robustly transitive skew-product with non-trivial, non-hyperbolic action on homology. The example is conservative, ergodic, non-uniformly…
Classification of partially hyperbolic diffeomorphisms under some rigid conditions
Pablo D. Carrasco, Enrique Pujals, Federico Rodriguez-Hertz
Consider a three dimensional partially hyperbolic diffeomorphism. It is proven that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and…
Random Products of Standard Maps
Pablo D. Carrasco
We develop a general geometric method to establish the existence of positive Lyapunov exponents for a class of skew products. The technique is applied to show non-uniform hyperboli…
Symbolic Dynamics for Normally Hyperbolic Foliations
Pablo D. Carrasco
We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well known methods available for uniformly hy…
Partially hyperbolic dynamics in dimension 3
Pablo Carrasco, Federico Rodriguez Hertz, Jana Rodriguez Hertz +1
Partial hyperbolicity appeared in the sixties as a natural generaliza- tion of hyperbolicity. In the last 20 years in this area there has been great activity. Here we survey the st…
Normally Hyperbolic Circle Foliations
Pablo D. Carrasco
In 1976 D. Sullivan gave an example of a flow on a compact manifold such that each one of its orbits is a circle and with the surprising property that there is no finite upper boun…
Non uniformly hyperbolic diffeomorphisms derived from the standard map
Pierre Berger, Pablo D. Carrasco
We prove that the system resulting of coupling the standard map with a fast hyperbolic system is robustly non-uniformly hyperbolic.
Compact Dynamical Foliations
Pablo D. Carrasco
According to the work of Dennis Sullivan, there exists a smooth flow on the 5-sphere all of whose orbits are periodic although there is no uniform bound on their periods. The quest…