Communications in Mathematical Physics

, Volume 125, Issue 2, pp 239–262 | Cite as

The thermodynamic formalism for expanding maps

  • David Ruelle


Letf:XX be an expanding map of a compact space (small distances are increased by a factor >1). A generating functionζ(z) is defined which countsf-periodic points with a weight. One can expressζ in terms of nonstandard “Fredholm determinants” of certain “transfer operators”, which can be studied by methods borrowed from statistical mechanics. In this paper we review the spectral properties of the transfer operators and the corresponding analytic properties ofζ(z). Gibbs distributions and applications to Julia sets are also discussed. Some new results are proved, and some natural conjectures are proposed.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Statistical Mechanic 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • David Ruelle
    • 1
  1. 1.I.H.E.S.Bures-sur-YvetteFrance

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