Abstract
We consider coupled map lattices of hyperbolic type, i.e., chains of weakly interacting hyperbolic sets (attractors) over multi-dimensional lattices. We describe the thermodynamic formalism of the underlying spin lattice system and then prove existence, uniqueness, mixing properties, and exponential decay of correlations of equilibrium measures for a class of Hölder continuous potential functions with a sufficiently small Hölder constant. We also study finite-dimensional approximations of equilibrium measures in terms of lattice systems (ℤ-approximations) and lattice spin systems (ℤd-approximations). We apply our results to establish existence, uniqueness, and mixing property of SRB-measures as well as obtain the entropy formula.
Original language | English (US) |
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Pages (from-to) | 675-711 |
Number of pages | 37 |
Journal | Communications In Mathematical Physics |
Volume | 193 |
Issue number | 3 |
DOIs | |
State | Published - 1998 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics