Noticias en español
Exponentes de Lyapunov y rigidez para difeomorfismos hiperbólicos y parcialmente hiperbólicos
ABSTRACT Voy a presentar unos resultados de rigidez en termino de exponentes de Lyapunov para difeomorfismos hiperbólicos y parcialmente hiperbólicos. Si un difeomorfismo hiperbólico (o parcialmente hiperbólico) es cerca a un automorfismo lineal (o un skew product sobre un automorfismo lineal), preserva el volumen, y tiene los mismos exponentes de Lyapunov (estables e inestable), entonces es suavemente conjugado al automorfismo lineal (o a un skew product sobre el automorfismo lineal). En el caso de difeomorfismos hiperbólicos el resultado puede ser visto como un análogo a la conjetura de...
Read MoreAlmost everywhere convergence of ergodic averages
ABSTRACT: In this talk I would like to discuss some of my results concerning almost everywhere convergence of non-conventional ergodic averages of L1 functions. These topics include: divergence of ergodic averages along the squares; convergence along some sequences of zero Banach density; convergence for arithmetic weights: the prime divisor functions ω and Ω.
Read MoreSistemas Dinámicos de Santiago Dynamical Day
Primera Sesión: 14:30 hrs. Speaker: Mike Todd (University of St Andrews, United Kingdom). Title: Phase transitions and limit laws. Abstract: The `statistics’ of a dynamical system is the collection of statistical limit laws it satisfies. This starts with Birkhoff’s Ergodic Theorem, which is about averages of some observable along orbits: this is a pointwise result, for typical points for a given invariant measure. Then we can look for forms of Central Limit Theorem, Large Deviations and so on: these are about how averages fluctuate, globally, with respect to the...
Read MoreDesvíos rotacionales para mapas del toro y aplicaciones.
ABSTRACT: El número de rotación de Poincaré es sin duda alguna el invariante más importante en el estudio dinámico de homeomorfismos del círculo (que preservan orientación). En general, estos sistemas exhiben lo que llamamos “desvíos rotacionales uniformemente acotados”, es decir, cualquier órbita de un homeomorfismo de este tipo siempre se mantiene a distancia uniformemente acotada de la órbita de la rotación rígida correspondiente. Esta importante propiedad tiene implicaciones profundas en dinámica unidimensional. En dimensiones superiores, en analogía con la teoría de...
Read MoreSensitive dependence of geometric Gibbs measures at positive temperature
ABSTRACT: In this talk we give the main ideas of the construction of the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states diverge at positive temperature. These are the first examples of divergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel....
Read MoreMorse theory for the action functional and a Poincare-Birkhoff theorem for flows
ABSTRACT: The goal of this talk is twofold. Firstly I would like to explain how pseudo-holomorphic curves can be used to study Morse theory of the action functional from classical mechanics. Then I will move to applications, focusing on a generalization of the Poincare-Birkhoff theorem for Reeb flows on the three-sphere.
Read More