Thermodynamic formalism Fall 2014
Math 36814
Instructors: Danny Calegari and Amie Wilkinson
TuTh 1:30-2:50; Eckhart 202
Description of course:
Cancellations:
November 6 class: field trip to Charles Smart's colloquium.
Notices:
None yet.
Syllabus:
The skeleton of the syllabus is the following.
- Classical thermodynamics
- Statistical mechanics
- Shannon's theory of information
- Equilibrium states for subshifts of finite type
- Axiom A dynamics
- Spectral gaps and dynamics
- Pressure and Hausdorff dimension
Notes from class and downloads:
Danny's introductory notes can be downloaded here and will be updated as we go along.
Encyclopedia article Smooth Ergodic Theory by Amie Wilkinson.
Notes from Amie's lectures (taken by Clark Butler):
10/9/14
10/23/14
11/4/14
11/11/14
11/13/14
11/18/14
11/20/14
11/25/14
12/2/14
References:
Physics:
- N. Davidson Statistical Mechanics, McGraw-Hill, New York, 1962
- E. Fermi Thermodynamics, Prentice-Hall, New York, 1937
- R. Feynman Statistical Mechanics; a set of lectures, Advanced book classics, Addison-Wesley, Reading, 1998
- J. von Neumann Mathematical foundations of quantum mechanics, Princeton landmarks in mathematics, Princeton University Press, Princeton, 1996
- A. Pippard The elements of Classical Thermodynamics, Cambridge University Press, Cambridge, 1957
- E. Schrodinger Statistical thermodynamics, Cambridge University, Cambridge, 1952
- C. Shannon A mathematical theory of communication, Bell system technical journal (July-October 1948) 27 (3): 379--423
Mathematics:
- R. Bowen Equilibrium states and the Ergodic theory of Anosov diffeomomorphisms Springer-Verlag LNM 470, Heidelberg, 1975
- D. Ruelle Thermodynamic formalism, Cambridge Mathematical Library, Cambridge University Press, Cambridge,
- O. Sarig Lecture notes on Thermodynamic formalism for topological Markov shifts Penn State, Spring 2009