Course Syllabus for

# Anisotropic Banach Spaces for Hyperbolic Dynamics Anisotropa Banachrum för hyperbolisk dynamik

## FMA155F, 4 credits

Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-08-24

## General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

## Aim

The aim is to give an introduction to the new and developing trend of using anisotropic Banach spaces to analyse statistical properties of hyperbolic dynamical systems. The goal is that the student should develop an understanding for the ideas behind these methods and to learn how they are used in simple cases.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must Understand how Ruelle transfer operators can be used to analyse statistical properties of dynamical systems and how anisotropic Banach spaces come in use to analyse the spectral properties of Ruelle transfer operators. The student must know how to use these techniques in simple cases.

Competences and Skills

For a passing grade the doctoral student must be able to explain how anisotropic banach spaces and Ruelle operators can be used to analyse hyperbolic dynamical systems, and to give overviews of proofs in simple settings.

Judgement and Approach

For a passing grade the doctoral student must be able to judge what are the pro and cons of various anisotropic Banach spaces in various situations.

## Course Contents

Anisotropic Banach spaces; Hyperbolic dynamics; Ruelle transfer operators.

## Course Literature

• Baladi, V.: The quest for the ultimate anisotropic Banach space. Journal of Statistical Physics, Springer Verlag, 2017.
• Baladi, V.: Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps: A Functional Approach. Springer, 2018. ISBN 9783319776606.

## Instruction Details

Type of instruction: Lectures

## Examination Details

Examination format: Oral exam