event
Thursday 14 Jun 2012: On the mixing properties of piecewise expanding maps under composition with permutations
Yiwei Zhang - CEMPS
Harrison 203 15:00-16:00
For a mixing and uniformly expanding interval map f on an interval I=[0,1) we pose
the following questions. For which permutation transformations, its composition with f is again mixing?
When the compostion is mixing, how does its mixing rate comparing with that of f ?
As a case study, we focus on the family of maps
f(x)=mx mod 1. We split the interval into N equal subintervals, and take permutations from S_N. We analyse those permutations for which
the composition is mixing, and show that, for large N, typical
permutations will preserve the mixing property. In contrast to the
situation for continuous time diffusive systems, we find that
composition with a permutation cannot improve the mixing rate, but
may make it worse. We obtain a precise result on the worst mixing
rate which can occur as permutations varies, with m, N fixed and
gcd(m,N)=1.
