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Über Gleichgewichtszustände der Druckfunktion

Equilibrium states for the pressure function

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Abstract

In this paper sufficient conditions for the existence of equilibrium states will be given. These conditions consist of topological assumptions for the underlying system which are linked with certain analytical properties of the given continuous function ϕ. It will be shown that the setV(T) which is defined byBowen in [1] is particularly suited to guarantee the existence of maximal measures. It is possible to show the following: Let 0≤ϕ∈V(T) and ϕ(x 0)=0 wherex 0 is a fixed point of the transformationT, and let\(\mathfrak{U}\) be a finite, open cover ofX, which satisfies.

$$\mathop {lim}\limits_{n \to \infty } \frac{{Q(T^n ,S_n \varphi ,(\mathfrak{U})_0^{n - 1} )}}{n} = P(T,\varphi )$$

Then there exists an equilibrium state for the pressure function.

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Literatur

  1. Bowen, R.: Some systems with unique equilibrium states. Math. Syst. Th.8, 193–202 (1974).

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  2. Denker, M., Chr. Grillenberger, andK. Sigmund: Ergodic Theory on Compact Spaces. Lecture Notes Math. 527. Berlin-Heidelberg-New York: Springer. 1976.

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  3. Hofbauer, F.: A function with countably many ergodic equilibrium states. Preprint. Wien. 1976.

  4. Walters, P.: A variational principle for the pressure of continuous transformations. Amer. J. Math.97, 937–971 (1975).

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Authors and Affiliations

  1. Institut für Mathematische Statistik und Wirtschaftsmathematik der Georg-August-Universität, Lotzestraße 13, D-3400, Göttingen, Bundesrepublik Deutschland

    Rolf Nürnberg

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  1. Rolf Nürnberg
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Nürnberg, R. Über Gleichgewichtszustände der Druckfunktion. Monatshefte für Mathematik 85, 125–136 (1978). https://doi.org/10.1007/BF01297542

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  • DOI: https://doi.org/10.1007/BF01297542

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