April 17, 2014

Thematic Program on Dynamics and Transport in Disordered Systems
January - June 2011 (Winter/Spring)

Seminars held at the Fields Institute

All courses will be held at the Fields Institute, Room 210 unless otherwise noted.

Program Visitors Seminars:

Thursday June 9
11 - 12 noon
Fields Institute, Room 210

Jacopo De Simoi
An application of standard pair techniques: bouncing ball systems in weak potentials


Thursday June 9
2 - 3 pm
Fields Institute, 3rd Floor Stewart Library
Peter Nandori
Central limit theorem for time-dependent dynamical systems
Tuesday April 26
2-3 pm
Fields Institute, 3rd Floor Stewart Library
Dimitry Turaev

Arnold difusion in a priori chaotic systems

Consider an analytic Hamiltonian system which has a chaoric behaviour (a horseshoe) in every energy level from a certain interval [a,b]. We show that a generic real-analytic time-periodic small perturbation of the Hamiltonian creates orbits for which the energy grows from a to b. This is a joint work with Gelfreich.

Thursday April 21
3:30 - 4:30 pm
Fields Institute, Room 210
Vaughn Climenhaga

Multifractal analysis and thermodynamics

Within a topological dynamical system, we study sets of trajectories characterised by their asymptotic behaviour. Such sets form a multifractal decomposition and are typically studied using either thermodynamic techniques (relying on the existence of continuously varying equilibrium states for certain potential functions) or saturation techniques (relying on some version of the specification property).

In the literature, saturation has been successfully used for a more general class of decompositions than thermodynamics. Each approach gives certain results that the other does not. I will describe the results obtained using each approach and present a new application of the thermodynamic approach, based on an idea of Hofbauer, that extends it to the same generality as the saturation approach.

Friday April 29
2-4 pm
Fields Institute, Room 210

Yakov Pesin

Thermodynamics associates to inducing schemes

Wednesday May 3
11 am
Fields Institute, Rm. 210

Tere M-Seara

Using two scattering maps to increase the angular momentum in the planar restricted 3-body problemD

Thursday May 5
3:30 - 5:30 pm
Fields Institute, 3rd Floor Stewart Library

Yakov Pesin

Essential coexistence of hyperbolic and completely non-hyperbolic behavior

Thursday May 12
11 am - 12 noon
Fields Institute, Room 210
Carlangelo Liverani

Exponential decay of correlation for piecewise cone hyperbolic contact flows

I will discuss some joint work with V.Baladi aiming at proving exponential decay of correlations for billiards flows. I will explain what we can achieve and what remains to be done.
Tuesday May 17
11-12 noon
Fields Institute, Room 210

Ke Zhang

The classical KAM theorem

I will present a sketch of the proof of the classical Kolmogorov-Arnold-Moser theorem. This is intended as an introduction to the next talk, where Sasa will talk about more modern results in this direction.

Tuesday May 24
11-12 noon
Fields Institute, Room 210

Sasa Kocic

Renormalization of vector fields and construction of KAM tori
Tuesday May 31
11 - 12 noon
Fields Institute, 3rd Floor Stewart Library

Amadeu Delshams

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

We consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Joint work with Gemma Huguet (Center for Neural Science).

Thursday June 2
10 - 11 am
Fields Institute, Room 210
Sasa Kocic

Renormalization of vector fields and construction of KAM tori (Part II)



Taking the Institute's Courses for Credit
As graduate students at any of the Institute's University Partners, you may discuss the possibility of obtaining a credit for one or more courses in this lecture series with your home university graduate officer and the course instructor. Assigned reading and related projects may be arranged for the benefit of students requiring these courses for credit.