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

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.