Noticias en español
Linear response formula for the topological entropy at the time one map of a geodesic flow on a manifold of negative curvature.
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.
Read MoreNotas sobre expansividad positiva para semiflujos continuos.
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.
Read MoreConjuntos Asintóticamente Seccional-Hiperbólicos.
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...
Read MoreBoundedness of hyperbolic components in moduli space.
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.
Read MoreAutomorphisms and extended symmetries of number-theoretic positive entropy subshifts.
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...
Read MoreHeterodimensionality of skew-products with concave fiber maps.
ABSTRACT: I will discuss examples of skew-products with concave interval fiber maps over a certain subshift. Here the subshift occurs as the projection of those orbits that stay in a given neighborhood and gives rise to a new type of symbolic space which is (essentially) coded. The fiber maps have expanding and contracting regions. As a consequence, the skew-product dynamics has pairs of horseshoes of different types of hyperbolicity. In some cases, they dynamically interact due to the superimposed effects of the (fiber) contraction and expansion, leading to nonhyperbolic dynamics...
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