- 03-202 Miaohua Jiang
- SRB Measures for Lattice Dynamical Systems
Apr 29, 03
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Abstract. For weakly coupled expanding maps
on the unit circle, Bricmont and Kupiainen showed that
the Sinai-Ruelle-Bowen (SRB) measure exists as a Gibbs state.
Via thermodynamic formalism, we prove that
this SRB measure is indeed the unique equilibrium state for a H\"older continuous
potential function on the infinite dimensional phase space.
For a more general class of lattice systems that are small perturbations
of the uncoupled map lattice, we present the variational principle, the entropy formula,
and the formula for the potential function for the SRB measures. For coupled
map lattices with nearest neighbor interactions, we give an explicit formula
of the potential function for the SRB measure and consequently, obtain
the entropy in terms of coupling parameters.