Equilibrium Measures for Coupled Map Lattices:¶Existence, Uniqueness and Finite-Dimensional Approximations

Nonequilibrium and Irreversibility

“…It can be shown that the basic results in [170,39,135]PS991BK996JP998 imply that if the "unperturbed dynamics" S 0 is smooth, hyperbolic, transitive (i.e. if S 0 is an Anosov map) then for ε small enough, but independently of the system size N , the system remains an Anosov map.…”

Uniqueness of the SRB Measure for Piecewise Expanding Weakly Coupled Map Lattices in Any Dimension

“…Starting with [7] numerous authors contributed to the exploration of ergodic and statistical properties of invariant measures for such systems, see e.g. [1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,29,31,32,34,35]. In all these publications the single site maps are hyperbolic or expanding (local) diffeomorphisms of a smooth manifold, and the coupling is modeled by a "diffeomorphism" of the infinite-dimensional state space.…”

A fluctuation theorem in a random environment

“…In this paper we follow the general ideas of the "cluster expansion" techniques which were introduced in [3][4][5][6][7] but developed following the tree expansion method of [1], see also [8].…”

“…The functions ψ ω , h ω can be split into two components along the vectors v ± : 5) and the equation (3.5) for h (1) ω,± gives…”