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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for Course FMA155F Anisotropic Banach Spaces for Hyperbolic Dynamics

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General
  • FMA155F
  • Temporary
Course Name
  • Anisotropic Banach Spaces for Hyperbolic Dynamics
Course Extent
  • 4
Type of Instruction
  • Third-cycle course
Administrative Information
  • 7151 (Centre of Mathematical Sciences / Mathematics)
  •  -08-24
  • Professor Thomas Johansson

Current Established Course Syllabus

General
  • English
  • If sufficient demand
  • Apply through e-mail
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.
Contents
  • Anisotropic Banach spaces; Hyperbolic dynamics; Ruelle transfer operators.
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.
Types of Instruction
  • Lectures
Examination Formats
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • Basic functional analysis. Knowledge about statistical properties of dynamical systems is usefull, but not necessary.
Selection Criteria
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.
Further Information
Course code
  • FMA155F
Administrative Information
  •  -08-24
  • Professor Thomas Johansson

All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Autumn 2018 2018‑05‑29 10:24:30 2018‑06‑07 13:45:29 2018‑08‑24

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