Take the 2-minute tour ×

Are there any good books out there that can serve as an introduction to thermodynamical formalism in dynamical systems?

I know only Zinsmeister's short "Thermodynamical formalism and holomorphic dynamical systems", which is concerned mostly with holomorphic dynamics, and Ruelle's "Thermodynamical formalism", which is, alas, too dense and has very little intuition. Any suggestions?

share|improve this question
add comment

3 Answers

up vote 4 down vote accepted

If you are interested in learning mathematical statistical physics (e.g. you would like to read Ruelle) then Minlos "Introduction to mathematical statistical physics" is a good choice for introduction to the area. If you would like to learn the part of ergodic theory which is called "thermodanamic formalism" and you don't care much about statistical physics then Omri Sarig's lecture notes is a great source http://www.math.psu.edu/sarig/TDFnotes.pdf

share|improve this answer
add comment

For an introduction I would recommend Thermodynamic Formalism and Holomorphic Dynamical Systems by Zinsmeister. It is short (75 pages excluding a small appendix and references), dates from 1996, and includes motivation.

You might also consider Thermodynamics of chaotic systems: an introduction by Beck and Schlogl, though SRB measures aren't introduced until quite late and the coverage is not at a mathematical level.

Ruelle also wrote a very short book called Chaotic Evolution and Strange Attractors that may be of interest, however his Reviews of Modern Physics article is very similar to this.

share|improve this answer
add comment

In my opinion the best basic text on the topic is

W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque, Vol {187-188} 1990

share|improve this answer
add comment

Your Answer


