Equilibrium states for lattice models of hyperbolic type
- 1 September 1995
- journal article
- research article
- Published by IOP Publishing in Nonlinearity
- Vol. 8 (5) , 631-659
- https://doi.org/10.1088/0951-7715/8/5/001
Abstract
We study the structural stability of coupled map lattice models of hyperbolic type under certain metrics. We prove the existence of equilibrium states for continuous functions on lattice models under the conditions of weak interaction and translation invariance. We also study the uniqueness and ergodic properties of these equilibrium states for Holder continuous functions.This publication has 9 references indexed in Scilit:
- Non-uniqueness of measures of maximal entropy for subshifts of finite typeErgodic Theory and Dynamical Systems, 1994
- Spatio-temporal chaos. III. Natural spatio-temporal measures for coupled circle map latticesNonlinearity, 1993
- Spatio-temporal chaos. II. Unique Gibbs states for higher-dimensional symbolic systemsNonlinearity, 1993
- Spatio-temporal chaos. I. Hyperbolicity, structural stability, spatio-temporal shadowing and symbolic dynamicsNonlinearity, 1993
- Transfer operators for coupled map latticesErgodic Theory and Dynamical Systems, 1992
- Spacetime chaos in coupled map latticesNonlinearity, 1988
- Possibility of high-temperature phase transitions due to the many-particle nature of the potentialTheoretical and Mathematical Physics, 1988
- Nonfinite perturbations of Gibbs fieldsTheoretical and Mathematical Physics, 1988
- The problem of uniqueness of a gibbsian random field and the problem of phase transitionsFunctional Analysis and Its Applications, 1969