Jon Chaika – Quantitative shrinking targets for IETs and rotations Quand 24 juin 2011 Ajouter au Calendrier Télécharger ICS Calendrier Google iCalendar Office 365 Outlook Live In this talk we present some quantitative shrinking target results. Consider $T:[0,1] \to [0,1]$. One can ask how quickly under $T$ a typical point $x$ approaches a typical point $y$. In particular given $\{a_i\}_{i=1}^{\infty}$ is $T^ix \in B(y,a_i)$ infinitely often? A finer question of whether $T^ix \in B(y,a_i)$ as often as one would expect will be discussed. That is, does $\lim_{N \to \infty} \frac{\sum_{n=1}^N \chi_{B(y,a_n)}(T^nx)}{\sum^N_{n=1} 2a_n}=1$ for almost every $x$. We will present applications to billiards in rational polygons and a related result for Sturmian sequences. This is joint work with David Constantine.
