Universität Wien

250123 VO Dynamische Systeme (Thermodynamischer Formalismus) (2012W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Donnerstag 11.10. 16:00 - 18:00 Seminarraum
  • Donnerstag 18.10. 16:00 - 18:00 Seminarraum
  • Donnerstag 25.10. 16:00 - 18:00 Seminarraum
  • Donnerstag 08.11. 16:00 - 18:00 Seminarraum
  • Donnerstag 15.11. 16:00 - 18:00 Seminarraum
  • Donnerstag 22.11. 16:00 - 18:00 Seminarraum
  • Donnerstag 29.11. 16:00 - 18:00 Seminarraum
  • Donnerstag 06.12. 16:00 - 18:00 Seminarraum
  • Donnerstag 13.12. 16:00 - 18:00 Seminarraum
  • Donnerstag 10.01. 16:00 - 18:00 Seminarraum
  • Donnerstag 17.01. 16:00 - 18:00 Seminarraum
  • Donnerstag 24.01. 16:00 - 18:00 Seminarraum
  • Donnerstag 31.01. 16:00 - 18:00 Seminarraum

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

Thermodynamic formalism is a mathematical approach to the theory, in statistical physics, on the way many-particle systems strive to configurations (called equilibrium states) of maximal entropy and minimal
potential energy. It is used to explain phase transitions in materials,
such as liquid vs. solid and magnitized vs. non-magnitized. Whereas in
physics, these ideas go back to Boltzmann in the late 19th century, it was
only in the 1970s that they were given a firm mathematical framework by
Sinai, Ruelle and Bowen. Topics of this course may include:
- Symbolic dynamics and subshifts of finite type.
- Entropy and the Variational Principle.
- The pressure function and phase transitions.
- Measures of maximal entropy.
- The Ising model and related models.
- Transfer operators and their spectral properties.
- Thermodynamics and fractal dimensions.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Prüfung und Übungsblätter

Mindestanforderungen und Beurteilungsmaßstab

Kenntnis und Verständnis der Lehrinhalte.

Prüfungsstoff

Vorlesung

Literatur

* Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag.
* Gerhard Keller, Equilibrium States in Ergodic Theory, Cambridge Univ. Press.
* Rufus Bowen, Equilibrium states and ergodic Theory of Anosov Diffeomorphisms, Springer-Verlag, Lect. Notes in Mathematics, 470, (1975).
* Omri Sarig, Lecture Notes on Thermodynamic Formalism for Topological Markov Shifts. Penn State, 2009.

Further texts:
* David Ruelle, Thermodynamic Formalism, Cambridge University Press, Cambridge, 2004.
* Vivianne Baladi, Positive Transfer Operators and Decay of Correlations, World Scientific Press.

Zuordnung im Vorlesungsverzeichnis

MSTV

Letzte Änderung: Mo 07.09.2020 15:40