Seminario de Sistemas Dinámicos

2009-03-25

Pär Kurlberg. (Kth)
Cursillo: Introduction to quantum ergodicity and arithmetic quantum maps
Sala D303 - Bachillerato- UC
Abstract:

El Cursillo se realizará los días Miércoles 25, Jueves 26 y viernes 27 de marzo de 2009 - 16:30 Hrs.

Resumen: The quantum mechanical counterpart to classical ergodicity is that eigenfunctions of the quantized Hamiltonian (stationary states)
should be equidistributed in a certain sense. If a dynamical system is classically ergodic, Schnirelman´s theorem asserts that most
stationary states are equidistributed. However, subsequences of exceptional eigenfunctions (scars) cannot be ruled out. On the other
hand, for some systems it seems reasonable to expect that no exceptional eigenfunctions exist, so called Quantum Unique Ergodicity
(QUE). Other expected consequences of classical chaos is that the value distribution of eigenfunctions, as well as the value
distribu

2009-03-23

Pär Kurlberg. Kth
Introduction to quantum ergodicity and arithmetic quantum maps
Auditorio Ninoslav Bralic - Fcultad de Matemáticas
Abstract:
The quantum mechanical counterpart to classical ergodicity is that
eigenfunctions of the quantized Hamiltonian (stationary states) should
be equidistributed in a certain sense. If a dynamical system is
classically ergodic, Schnirelman´s theorem asserts that most
stationary states are equidistributed. However, subsequences of
exceptional eigenfunctions (scars) cannot be ruled out. On the other
hand, for some systems it seems reasonable to expect that no
exceptional eigenfunctions exist, so called Quantum Unique Ergodicity
(QUE). Other expected consequences of classical chaos is that the
value distribution of eigenfunctions, as well as the value
distribution of matrix coefficients of observables, should be
Gaussian.

2009-03-23

Joseph Silverman. Brown University
Specialization Theorems in Dynamics
Auditorio Ninoslav Bralic -15:30 Hrs - Facultad de Matemáticas
Abstract:
Abstract: A common mathematical problem is to take a family of objects (spaces, maps, etc.) and ask to what extent the particular members of the
family retain the properties of the family as a whole. For example,
let F(T;z) be a one-parameter family of rational functions of degree
at least two, a typical example being F(T;z) = z2 + T. Further let
P(T) be a one-parameter family of initial points with the property
that P(T) has infinite forward orbit under iteration of F(T;z). If
F(T;z) and P(T) have coefficients in a number field K, then one can
show that there are only finitely many t in K such that the
specialized point P(t) has finite order under iteration of the
specialized map F(t;z). This is a typical specialization theorem. In
this talk I will discuss this theorem, give an application to
post-critically finite maps, and describe conjectural analogues for
higher-dimensional families.

2009-03-06

Renaud Leplaideur. Université de Brest
Renormalization and virtual Manneville-Pomeau maps
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

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2009-01-26

Yoshifumi Matsuda. Universidad de Tokyo
The Rotation Number Function on Groups of Real-Analytic Diffeomorphisms of The Circle
Fac. de Ciencias de la U. de Chile (Las Palmeras) - 16:30 Hrs.

2009-01-19

Karl Petersen. (Unc)
Sturmian and adic symbolic dynamics from the Farey-Stern-Brocot diagram.
CMM - SALA PISO 7 - 17:00 a 18:00 Hrs.
Abstract:

Abstract: A slight modification of the Farey or Stern-Brocot tree produces a Bratteli diagram and therefore an associated  Bratteli-Vershik adic dynamical system. All Sturmian systems

shows us the lexicographically minimal sequences in Sturmian

lexicographic order of 0,1 sequences here and in beta-shifts,

properties appears.

2009-01-19

Pascale Roesch. U. de Toulouse, Francia
The Boundary of Bounded Polynomial Fatou Components
CMM - SALA PISO 7 - 15:30 a 16:30 Hrs.

2008-12-22

Gabriela Fernández. Impa, Brasil
Flujos Holomorfos Dicríticos en Superficies de Stein
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

Estudiaremos la clasificación del par (

M,X) donde M es una superficie de Stein y X un campo vectorial holomorfo completo en M. Mostraremos que si M es un superficie con H2(M, Z) = 0 y X tiene una singularidad dicríptica, entonces M es biholomorfa a C2 y el campo X es globalmente linearizable."

2008-12-01

Fabien Duran. Université de Picardie
Rauzy fractal in $R imes C$.
USACH - Sala por confirmar
Abstract:
Abstract: The Rauzy fractal is a well-known object living in $C$ carrying a lot of questions/problems in number theory, dynamical systems, numeration
systems, automata theory, hausdorff dimension, tilings, etc ...
Almost nothing is known for such object in $R imes C$.
We will present some first results in this direction. More specifically,
we will look at the Rauzy fractal generated by the polynomial
P(x)=x⁴-x³-x²-x-1.
"

2008-11-21

Neil Dobbs. Kth
Hyperbolic Dimension for Interval Maps
Sala N-31 Campus San Joaquín - UC
Abstract:
Abstract: The hyperbolic and Hausdorff dimensions are shown to coincide for $C2$ maps without recurrent critical points. The maps
may have parabolic periodic points. The Julia set for certain such maps may have hyperbolic dimension equal to 1 but Lebesgue measure
equal to 0.