Invariant Measures and Equilibrium States for Some Mappings which Expand Distances
Open Access
- 1 February 1978
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 236, 121-153
- https://doi.org/10.2307/1997777
Abstract
For a certain collection of transformations T we define a Perron-Frobenius operator and prove a convergence theorem for the powers of the operator along the lines of the theorem D. Ruelle proved in his investigation of the equilibrium states of one-dimensional lattice systems. We use the convergence theorem to study the existence and ergodic properties of equilibrium states for T and also to study the problem of invariant measures for T. Examples of the transformations T considered are expanding maps, transformations arising from f-expansions and shift systems.Keywords
This publication has 11 references indexed in Scilit:
- Equilibrium States and the Ergodic Theory of Anosov DiffeomorphismsPublished by Springer Nature ,1975
- Bernoulli equilibrium states for axiom A diffeomorphismsTheory of Computing Systems, 1974
- Anosov flows with gibbs measures are also BernoullianIsrael Journal of Mathematics, 1974
- A number-theoretic class of weak Bernoulli transformationsTheory of Computing Systems, 1973
- On isomorphism of weak Bernoulli transformationsAdvances in Mathematics, 1970
- Two Bernoulli shifts with infinite entropy are isomorphicAdvances in Mathematics, 1970
- Endomorphisms of Compact Differentiable ManifoldsAmerican Journal of Mathematics, 1969
- Statistical mechanics of a one-dimensional lattice gasCommunications in Mathematical Physics, 1968
- Exact endomorphisms of a Lebesgue spacePublished by American Mathematical Society (AMS) ,1964
- Representations for real numbers and their ergodic propertiesActa Mathematica Hungarica, 1957