|
Local product structure for Equilibrium States
Author(s):
Renaud
Leplaideur
Journal:
Trans. Amer. Math. Soc.
352
(2000),
1889-1912.
MSC (2000):
Primary 37D20, 37D35
Posted:
November 17, 1999
MathSciNet review:
1661262
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using different kinds of extensions the local product structure of Gibbs-measure is proven.
References:
- 1.
- M. Babillot and F. Ledrappier, Geodesic paths and horocycle flow on abelian covers, Centre de Mathématiques de l'École Polytechnique.
- 2.
- L. Barreira, Y. Pesin, and J. Schmeling, Dimension of hyperbolic measures - A proof of the Eckmann-Ruelle conjecture, Weierstraß-Institut für Angewandte Analysis und Stochastik, 1996.
- 3.
- R. Bowen, Some Systems with Unique Equilibrium States, Mathematical Systems Theory 8 (1974), no. 3, 193-202. MR 53:3257
- 4.
- -, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math., vol. 470, Springer-Verlag, 1975. MR 56:1364
- 5.
- R. Bowen and B. Marcus, Unique Ergodicity for Horocycle Foliations, Israel Journal of Mathematics 26 (1977), no. 1, 43-67. MR 56:9594
- 6.
- A. Broise, F. Dal'bo, and M. Peigné, Méthode de opérateurs de transferts : Transformations dilatantes de l'intervalle et dénombrement de géodésiques fermées.
- 7.
- Yael Naim Dowker, Finite and
 -finite invariant measures, Annals of Mathematics 54 (1951), no. 3, 595-608. MR 13:543a - 8.
- Nicolai T.A. Haydn, Canonical product structure of equilibrium states, Random and Computational Dynamics 2 (1994), no. 1, 79-96. MR 95c:58133
- 9.
- N.T.A. Haydn and D. Ruelle, Equivalence of Gibbs and Equilibrium States for Homeomorphisms Satisfying Expansiveness and Specification, Commun. Math. Phys. 148 (1992), 155-167. MR 93h:58084
- 10.
- C.T. Ionescu Tulcea and G. Marinescu, Théorie ergodique pour des classes d'opérations non complètement continues, Annals of Mathematics 52 (1950), no. 1, 140-147. MR 12:266g
- 11.
- F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms Part I: Characterization of measures satisfying Pesin's entropy formula, Annals of Mathematics 122 (1985), 509-539. MR 87i:58101a
- 12.
- -, The metric entropy of diffeomorphisms Part II: Relations between entropy,exponents and dimension, Annals of Mathematics 122 (1985), 540-574. MR 87i:58101b
- 13.
- V.A. Rohlin, On the fundamental ideas of measure theory, A.M.S.Translation 10 (1962), 1-52. MR 11:18f; MR 13:924e
- 14.
- Walter Rudin, Real and Complex Analysis, Third edition, McGraw-Hill Book Company, 1987.MR 88k:00002
- 15.
- D. Ruelle, Thermodynamic formalism for maps satisfying positive expansiveness and specification, Nonlinearity 5 (1992), 1223-1236. MR 94a:58115
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
37D20, 37D35
Retrieve articles in all Journals with
MSC (2000):
37D20, 37D35
Additional Information:
Renaud
Leplaideur
Affiliation:
Laboratoire de Mathématique et Applications des Mathématiques, Université de Bretagne-Sud, 1, rue de la Loi, 56000 Vannes, France
Email:
Renaud.Le-Plaideur@univ-ubs.fr
DOI:
10.1090/S0002-9947-99-02479-4
PII:
S 0002-9947(99)02479-4
Received by editor(s):
June 30, 1997
Posted:
November 17, 1999
Copyright of article:
Copyright
2000,
American Mathematical Society
|
