Seminario de Sistemas Dinámicos

2008-05-05

Eugenio Trucco. Universidad de Chile
Conjuntos de Julia Algebraicos y Dominios de Fatou Errantes
Fac. de Ciencias, Depto. de Matemáticas (Las Palmeras) Universidad de Chile

2008-04-21

Godofredo Iommi. Pontificia Universidad Católica de Chile
Multifractal analysis for the backward continued fraction map.
Por confirmar
Abstract:
Abstract: In this talk I will discuss the multifractal spectrum of
Lyapunov exponents for interval maps with infinitely many branches and a
parabolic fixed point. It turns out that, in strong contrast with the
hyperbolic case, the domain is unbounded and points of
non-differentiability might exist. We also study the thermodynamic
formalism for such maps. We describe the pressure function and prove
existence and uniqueness of equilibrium measures. In order to do so, we
introduce a countable Markov shift that can be thought of as a
generalisation of the renewal shift.

2008-04-18

Mario Ponce. Pontificia Universidad Católica de Chile
Invariant continua for fibered germs
Sala 7 Block A, Departamento de Fisica USACH, a las 16:30 hrs.
Abstract:
Abstract: We will survey some of the classical and recent results about the Perez-Marco continua attached to an invariant fixed point for a holomorphic germ. We will sketch the proof of an analogous existence result in the fibered setting. We will state some open questions about this fibered invariant set.

2008-04-14

Bartlomiej Skorulski. Universidad Católica del Norte
Geometría de Conjuntos Aleatorios.
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.

2008-04-07

José Aliste. Dim - Nice.
Translations numbers for maps of the real with pattern- equivariant displacement
Sala de Seminarios CMM - 17:00 Hrs.
Abstract:
Abstract:
We study translation theory for non-decreasing maps of the real line with a pattern-equivariant displacement with respect to a quasicrystal. We use the correspondence between pattern-equivariant functions and continuous functions over the continuous hull associated with the quasicrystal to settle down and prove our results. First, we prove the existence of translation numbers using Kakutani-Rokhlin towers for maps without fixed points.
Second, we investigate the question of existence of a semiconjugacy
between such a map and a translation, and we concentrate in semiconjugacies that also have pattern-equivariant displacements. Under a boundedness condition, we prove a generalization of the Poincaré Theorem, finding a sufficient condition for such a semicon

2008-04-06

Genadi Levin. Hebrew University
Multipliers of Periodic Orbits.
Sala 2 (Víctor Ochsenius) - Fac. de Matemáticas - 16:30 Hrs.
Abstract: