Sinai-Ruelle-Bowen Measures for Lattice Dynamical Systems

摘要: For weakly coupled expanding maps on the unit circle, Bricmont and Kupiainen showed that Sinai-Ruelle-Bowen (SRB) measure exists as a Gibbs state. Via thermodynamic formalism, we prove this SRB is indeed unique equilibrium state for Holder continuous potential function infinite dimensional phase space. more general class of lattice systems are small perturbations uncoupled map lattice, present variational principle, entropy formula, formula measures. lattices with nearest neighbor interactions, give an explicit consequently, obtain in terms coupling parameters.