Relatively invariant measures

‎On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

On Relatively Nonatomic Measures

Exploring invariant sets and invariant measures.

We propose a method to explore invariant measures of dynamical systems. The method is based on numerical tools which directly compute invariant sets using a subdivision technique, and invariant measures by a discretization of the Frobenius-Perron operator. Appropriate visualization tools help to analyze the numerical results and to understand important aspects of the underlying dynamics. This w...

Invariant Measures for aTwo

We consider a process of two classes of particles jumping on a one dimensional lattice. The marginal system of the rst class of particles is the one dimensional totally asymmetric simple exclusion process. When classes are disregarded the process is also the totally asymmetric simple exclusion process. The existence of a unique invariant measure with product marginals with density and for the r...

Averaging and Invariant Measures

An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along the leaves of this foliation [44], [46], [38]. We review recent results on this subject and present some extensions and open questions. 2000 Math. Subj. Class. Primary 34C29; Secondary 37D30.