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Friday, March 28, 2014 - 13:05 ,
Location: Skiles 005 ,
Lei Zhang ,
Georgia Tech ,
Organizer:

We present the proof of the Shannon-McMillan-Breiman Theorem. This is part of a reading seminar geared towards understanding of Smooth
Ergodic Theory. (The study of dynamical systems using at the same time
tools from measure theory and from differential geometry)It should be
accesible to graduate students and the presentation is informal. The
first goal will be a proof of the Oseledets multiplicative ergodic
theorem for random matrices. Then, we will try to cover the Pesin
entropy formula, invariant manifolds, etc.

Friday, March 14, 2014 - 13:05 ,
Location: Skiles 005 ,
Lei Zhang ,
Georgia Institute of Technology ,
Organizer:

We introduce concepts of entropy and methods of calculation of entropy and examples. This is part of a reading seminar geared towards understanding of Smooth Ergodic Theory. (The study of dynamical systems using at the same time tools from measure theory and from differential geometry)It should be accesible to graduate students and the presentation is informal. The first goal will be a proof of the Oseledets multiplicative ergodic theorem for random matrices. Then, we will try to cover the Pesin entropy formula, invariant manifolds, etc.

Friday, March 7, 2014 - 13:00 ,
Location: Skiles 05 ,
Mikel J. de Viana ,
Georgia Tech ,
Organizer: Rafael de la Llave

We will present a proof of the subadditive ergodic theorem. This is part of a reading seminar geared towards understanding of Smooth Ergodic Theory. (The study of dynamical systems using at the same time tools from measure theory and from differential geometry)It should be accesible to graduate students and the presentation is informal. The first goal will be a proof of the Oseledets multiplicative ergodic theorem for random matrices. Then, we will try to cover the Pesin entropy formula, invariant manifolds, etc.

Friday, February 28, 2014 - 13:00 ,
Location: Skiles 005 ,
Lei Zhang ,
Georgia Tech ,
lzhang98@math.gatech.edu ,
Organizer: Lei Zhang

This is a reading seminar on smooth ergodic theory. In the first talk we will introduce some basic notions of ergodic theory and proof Birkhoff Ergodic Theorem.

Tuesday, November 19, 2013 - 16:05 ,
Location: Skiles 005 ,
Mikel J. de Viana ,
Georgia Tech ,
Organizer:

We conclude the proof of the linearization theorem for fibered holomorphic maps by showing that the iteration scheme we proposed converges. If time allows, we will comment on related work by Mario Ponce and generalizations of the theorem for fibered holomorphic maps in higher dimensions.

Tuesday, November 12, 2013 - 15:00 ,
Location: Skiles 06 ,
Mikel J. de Viana ,
Georgia Tech ,
Organizer: Rafael de la Llave

Given f: \C \times T^1 to itself, an analytic perturbation of a fibered
rotation map , we will present two proofs of
existence of an analytic conjugation of f to the fibered rotation
, on a neighborhood of {0} \times T^1. This talk will
be self- contained except for some usual "tricks" from KAM theory and
which will be explained better in another talk. In the talk we will
discuss carefully the number theoretic conditions on the fibered
rotation needed to obtain the theorem.

Tuesday, October 29, 2013 - 15:05 ,
Location: Skiles 06 ,
Chongchun Zeng ,
Georgia Tech ,
Organizer: Rafael de la Llave

Incompressible Euler equation is known to be the geodesic flow on the
manifold of volume preserving maps. In this informal seminar, we will
discuss how this geometric and Lagrangian point of view may help us
understand certain analytic and dynamic aspects of this PDE.

Monday, October 21, 2013 - 15:05 ,
Location: Skiles 006 ,
Chongchun Zeng ,
Georgia Tech ,
Organizer: Rafael de la Llave
Incompressible Euler equation is known to be the geodesic flow on the
manifold of volume preserving maps. In this informal seminar, we will
discuss how this geometric and Lagrangian point of view may help us
understand certain analytic and dynamic aspects of this PDE.

Wednesday, October 16, 2013 - 15:05 ,
Location: Skiles 006 ,
Chongchun Zeng ,
Georgia Tech ,
Organizer: Chongchun Zeng
Incompressible Euler equation is known to be the geodesic flow on the manifold of volume preserving maps. In this informal seminar, we will discuss how this geometric and Lagrangian point of view may help us understand certain analytic and dynamic aspects of this PDE.

Tuesday, October 8, 2013 - 16:05 ,
Location: skiles 006 ,
Mikel J. de Viana ,
Georgia Tech ,
Organizer:
Given f: \C \times T^1 to itself, an analytic perturbation of a fibered rotation map , we will present two proofs of existence of an analytic conjugation of f to the fibered rotation , on a neighborhood of {0} \times T^1. This talk will be self- contained except for some usual "tricks" from KAM theory and which will be explained better in another talk. In the talk we will discuss carefully the number theoretic conditions on the fibered rotation needed to obtain the theorem.