Dynamical Systems

Invariant Family of Leaf measures and The Ledrappier-Young Property for Hyperbolic Equilibrium States.

Event Date: Apr 12, 2021 in Dynamical Systems, Seminars

ABSTRACT: Let be a Riemannian, boundaryless, and compact manifold with , let be a () diffeomorphism of , and let be a Hölder continuous potential on . We construct an invariant and absolutely continuous family of measures (with transformation relations defined by ), which sit on local unstable leaves. We present two main applications. First, given an ergodic homoclinic class , we prove that admits a local equilibrium state on if and only if is “recurrent on ” (a condition tested by counting periodic points), and one of the leaf measures gives a positive measure to a set of...

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Equivalencia orbital fuerte y complejidad factorial en subshifts.

Event Date: Dec 16, 2020 in Dynamical Systems, Seminars

ABSTRACT: Dos sistemas dinámicos topológicos se dicen orbitalmente equivalentes cuando existe un homemorfismo entre los espacios de fase que envía órbitas en órbitas. Dado un subshift minimal, su complejidad factorial es la función $p_X: \N \to \N$ que cuenta el número de cilindros no vacíos de largo $n$. En esta charla discutiremos sobre cómo la complejidad factorial posiblemente restringe las clases de equivalencia orbital (fuerte) para subshifts minimales. Trabajo conjunto con S. Donoso.

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Linear response formula for the topological entropy at the time one map of a geodesic flow on a manifold of negative curvature.

Event Date: Dec 02, 2020 in Dynamical Systems, Seminars

ABSTRACT Let be the time one map of a geodesic flow on a manifold of constant negative curvature with its Liouville measure. Consider , a family of diffeomorphisms with . In this talk we discuss about the differentiability of the map at , and we provide an explicit formula for its derivative.

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Notas sobre expansividad positiva para semiflujos continuos.

Event Date: Nov 25, 2020 in Dynamical Systems, Seminars

ABSTRACT: En esta charla probaremos que si X es un espacio métrico y $\phi$ es un semiflujo continuo positivamente expansivo, en el sentido de Alves, Carvalho y Siqueira (2017), entonces el semiflujo $\phi$ es trivial y el espacio X es uniformemente discreto. En particular, si X es compacto, entonces es un conjunto finito.

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Conjuntos Asintóticamente Seccional-Hiperbólicos.

Event Date: Nov 18, 2020 in Dynamical Systems, Seminars

ABSTRACT: La noción de conjunto Asintóticamente Seccional-Hiperbólico fue introducida en [1] por C. Morales y B. San Martín. La principal característica que presentan estos conjuntos es que cualquier punto fuera de las variedades estables de sus singularidades (las cuales son hiperbólicas) poseen tiempos hiperbólicos arbitrariamente grandes. Ejemplos de sistemas que verifican esta clase de hiperbolicidad son la Herradura Singular Contractiva [1], el atractor exhibido en [2] y el atractor de Rovella [3]. En esta charla se presentarán algunas propiedades dinámicas que satisfacen estos...

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Boundedness of hyperbolic components in moduli space.

Event Date: Nov 11, 2020 in Dynamical Systems, Seminars

ABSTRACT: A complex rational map of degree at least 2 is hyperbolic if each of its critical points is attracted to an attracting cycle. For a fixed degree, the hyperbolic rational maps form an open set in the space of rational maps. This open set deduces an open set in the moduli space of rational maps, modulo the Möbius conjugacy. Each component of the deduced open set is a hyperbolic component. In this talk, I will present some precompactness results on hyperbolic components. In particular, I will focus on the space of quartic Newton maps. This is a joint work with Y. Gao.

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