Dynamical Systems - Summer School

Problem Sets

for Basic Ergodic Theory by Omri Sarig:

Problem set for lectures 1 to 4 (7/6/2015)

Suggested readings

An introduction to small divisor problems by Stefano Marmi
Celestial Mechanics, Part I by Shlomo Sternberg
The conceptual foundations of the statistical approach in Mechanics by Paul and Tatiana Ehrenfest
Chaotic behaviour in the solar system by S. Marmi
Ergodicity, ensembles, irreversibility in Boltzmann and beyond by G. Galavotti (about the etymology of the word "ergodic").
Continued Fractions by A. Khinchin
The multifarious Poincaré recursion Theorem by V. Bergelson
Some Historical Remarks and Modern Questions Around The Ergodic Theorem by V. Bergelson
Les Méthodes Nouvelles de la Mécanique Céleste by H. Poincaré.

Lecture Notes (not proof-read)

We thank the various participants who kindly provided notes.

for Basic Ergodic Theory by Omri Sarig:

Lecture 1 (notes by Miguel Moreira, 7/6/2015)
Lecture 1 (notes by Myriam Aquino, 7/6/2015)
Lectures 2 and 3 (notes by Myriam Aquino, 7/7/2015)
Lectures 2 and 3 (notes by Luís Duarte, 7/7/2015)
Lecture 4 (notes by Miguel Moreira, 8/7/2015)
Lecture 5 (notes by Andreia Chapouto, 7/10/2015)

for An introduction to small divisor problems by Stefano Marmi:

Lecture 1 (notes by Miguel Moreira, 7/6/2015)
Lecture 1 (notes by Myriam Aquino, 7/6/2015)
Lecture 2 (notes by Miguel Moreira, 7/7/2015)
Lectures 3 and 4 (notes by Miguel Moreira, 7/9/2015)
Lectures 3 and 4 (notes by Luís Duarte, 7/9/2015)
Lecture 5 (notes by Andreia Chapouto, 7/10/2015)

for Uniform distribution, dynamics and Diophantine problems by Vitaly Bergelson :

Lecture 1 (notes by Maria Inês Couto, 7/6/2015)
Lectures 2 and 3 (notes by Miguel Moreira, 7/8/2015)
Lecture 4 (notes by Francisco Machado, 7/9/2015)
Lecture 5 (notes by Andreia Chapouto, 7/10/2015)