Dynamical Systems

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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Automorphisms and extended symmetries of number-theoretic positive entropy subshifts.

Event Date: Nov 04, 2020 in Dynamical Systems, Seminars

ABSTRACT: We will discuss one- and multidimensional subshifts constructed via number-theoretically defined subsets of the integers (e.g. the visible lattice points in the plane, k-free integers, etc.), focusing our interest on their groups of automorphisms and extended symmetries, which are naturally defined conjugacy invariants. This type of shift space exhibits symmetry rigidity (that is, its group of automorphisms is essentially trivial), but is compatible with positive entropy and shows interesting variations on their extended symmetry groups, which may be small (finite) or large...

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