Canonical product structure of equilibrium states. (English) Zbl 0810.58030

Haydn, Nicolai T. A.

Random Comput. Dyn. 2, No. 1, 79-96 (1994).

The author’s abstract: “It will be shown that on the stable and unstable foliations of Axiom A flows there exists, associated to Hölder continuous potentials, transversal measures that satisfy smooth Margulis’ type cocycle equations. Using these transversal measures, one then deduces that equilibrium states for Hölder continuous potentials are indeed of product form. It is then also shown that in the case of a suspended flow over a subshift of finite type, there are, corresponding to the poles of the weighted zeta function, transversal distributions which satisfy Margulis’ type cocycle equations similar to the ones for the transversal measures”.

Reviewer: J.Ombach (Kraków)

MSC:

37D99	Dynamical systems with hyperbolic behavior
82B30	Statistical thermodynamics

Keywords:

Margulis measures; Axiom A flows; equilibrium states; Hölder continuous potentials