A criterion for weak mixing of induced interval exchange transformations

Abstract

Let $f:X\to X$, $X=[0,1)$, be an ergodic IET (interval exchange transformation) relative to the Lebesgue measure on $X$. Denote by $f_t:X_t\to X_t$ 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.

12 pages

References in corpus (2)

• A note on zero-one laws in metrical Diophantine approximation
• Borel-Cantelli sequences