Abstract
We study Axiom A flows and introduce a new definition of Gibbs states which is modeled after a current one for diffeomorphisms and by which Gibbs states are locally characterized by their transformation when pulled back by conjugating homeomorphisms. We show that Gibbs states are equilibrium states and vice versa. We also show that for subshifts this equivalence can be strengthened.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. M. Abramov, On the entropy of a flow,Doklady Akad. Nauk SSSR 128:873–876 (1959);Am. Math. Soc. Transl. (2)49:167-170 (1966).
R. Bowen, Symbolic dynamics for hyperbolic flows,Am. J. Math. 95:429–160 (1973).
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows,Invent. Math. 29:181–202 (1975).
R. Bowen and P. Walters, Expansive one-parameter flows,J. Diff. Equations 12:180–193 (1972).
D. Capocaccia, A definition of Gibbs states for a compact set withZ v-action,Commun. Math. Phys. 48:85–88 (1976).
N. T. A. Haydn, Canonical product structure of equilibrium states, preprint.
N. T. A. Haydn, Classification of Gibbs states for Axiom A diffeomorphisms and one-dimensional lattice systems, preprint.
N. T. A. Haydn, On Gibbs and equilibrium states,Ergod. Theory Dynam. Syst. 7:119–132 (1987).
D. Ruelle,Thermodynamic Formalism (Addison-Wesley, 1978).
P. Walters,An Introduction to Ergodic Theory (Springer, 1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haydn, N.T.A. Gibbs measures for Axiom A flows. J Stat Phys 72, 309–327 (1993). https://doi.org/10.1007/BF01048052
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01048052