# セミナー

## 力学系セミナー

タイトル Escape rate in one-dimensional dynamics 2015年6月9日 13:00-14:30 高橋 博樹 氏（慶應・数理） 矢上キャンパス14棟537 We consider a multimodal interval map of class $C^3$, together with an invariant set which is maximal in a closed interval and allowed to contain critical points. Under mild assumptions, we show that the rate of escape from the interval is given by the pressure associated with the geometric potential. We also show that, if the Lyapunov exponents of all invariant Borel probability measures are uniformly bounded away from zero, then the Hausdorff dimension of the invariant set is given by the zero of the pressure equation. A main tool is {\it the horseshoe extract argument} based on {\it the uniform scale lemma} of Juan Rivera-Letelier.