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A criterion for weak mixing of induced interval exchange transformations

By M. Boshernitzan

Abstract

Let $f\colon X\to X$, $X=[0,1)$, be an ergodic IET (interval exchange transformation) relative to the Lebesgue measure on $X$. Denote by $f_t\colon X_t\to X_t$ the IET obtained by inducing $f$ to the subinterval $X=[0,t)$, $0<t<1$. We show that \[ \{0<t<1\mid f_{t} \text{is weakly mixing}\} \] is a residual subset of $X$ of full Lebesgue measure. The result is proved by establishing a generic Diophantine sufficient condition on $t$ for $f_{t}$ to be weakly mixing.Comment: 12 page

Topics: Mathematics - Dynamical Systems, Mathematics - Number Theory, Mathematics - Probability, 37E05, 37A55
Year: 2011
OAI identifier: oai:arXiv.org:1105.0239
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