FMA155F

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Anisotropic Banach Spaces for Hyperbolic Dynamics

4

Ren forskarutbildningskurs

7151 (Matematikcentrum (inst LTH) / Matematik (LTH))

 -08-24

Professor Thomas Johansson

Engelska

Vid tillräcklig efterfrågan

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.

Anisotropic Banach spaces; Hyperbolic dynamics; Ruelle transfer operators.

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.

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.

be able to judge what are the pro and cons of various anisotropic Banach spaces in various situations.

Föreläsningar

Muntlig tentamen

Underkänd, godkänd

Basic functional analysis. Knowledge about statistical properties of dynamical systems is usefull, but not necessary.

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.

FMA155F

 -08-24

Professor Thomas Johansson