Disjointness of interval exchange transformations from systems of probabilistic origin

Details Disjointness of interval exchange transformations from systems of probabilistic origin Disjointness of interval exchange transformations from systems of probabilistic origin

2009-08-02

arxiv.org/abs/0908.0140v1

Mathematics

Dynamical Systems

20 pages, 1 figure. Paper accepted in DCDS-A

Scientific paper

It is proved that almost every interval exchange transformation given by the symmetric permutation 1->m, 2->m-1,..., m-1->2, m->1, where m>1 is an odd number, is disjoint from ELF systems. The notion of ELF systems was introduced to express the fact that a given system is of probabilistic origin; the following standard classes of systems of probabilistic origin enjoy the ELF property: mixing systems, ergodic Gaussian systems, Poisson suspensions, dynamical systems coming from stationary infinitely divisible processes. Some disjointness properties of special flows built over interval exchange transformations and under piecewise constant roof function are investigated as well.

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