Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps

Sinai-Ruelle-Bowen Measures for Lattice Dynamical Systems

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 Hölder continuous potential function on the infinite dimensional phase space. For a more general class of lattice systems that are small pert...

SRB measures for certain almost hyperbolic diffeomorphisms

Conformal measures for multidimensional piecewise invertible maps

Given a piecewise invertible map T : X → X and a weight g : X →]0,∞[, a conformal measure ν is a probability measure on X such that, for all measurable A ⊂ X with T : A→ TA invertible, ν(TA) = λ ∫

Finite Approximation of Sinai-Bowen-Ruelle Measures for Anosov Systems in Two Dimensions

We describe a computational method of approximating the \physical" or Sinai-Bowen-Ruelle measure of an Anosov system in two dimensions. The approximation may either be viewed as a xed point of an approximate Perron-Frobenius operator or as an invariant measure of a randomly perturbed system.

Periodicity of certain piecewise affine planar maps

In the past few decades, discontinuous piecewise affine maps have found considerable interest in the theory of dynamical systems. For an overview, we refer the reader to [1, 7, 12, 13, 17, 18], for particular instances to [29, 16, 25] (polygonal dual billiards), [15] (polygonal exchange transformations), [10, 31, 11, 8] (digital filters) and [19, 21, 22] (propagation of round-off errors in line...