Analytic and quasi-invariant measures

Admissible vector fields and quasi-invariant measures∗

Invariant Measures for Real Analytic Expanding Maps

Let X be a compact connected subset of Rd with non-empty interior, and T : X → X a real analytic full branch expanding map with countably many branches. Elements of a thermodynamic formalism for such systems are developed, including criteria for compactness of transfer operators acting on spaces of bounded holomorphic functions. In particular a new sufficient condition for the existence of a T ...

Quasi-analytic Vectors and Quasi-analytic Functions

Quasi-Monte Carlo in the Parallel Computation of Invariant Measures

For a non-singular multi-dimensional mapping S: X Æ X, the corresponding FrobeniusPerron operator is P. In the paper, the schemes for generating the quasi-random numbers are studied for the parallel computation for the fixed density of P. The numerical results for these schemes are presented.

Parallel Quasi-Monte Carlo Computation of Invariant Measures

where m is the Lebesgue measure of R, has a fixed density f∗. This fixed density gives rise to a physical measure of S, which describes the asymptotic behavior of the chaotic orbits from the statistical viewpoint [3]. Our purpose is efficient computation of such fixed densities. In his book [6], Ulam proposed a piecewise constant approximation method to calculate the fixed density f∗ and conjec...