授课地点：纯水楼301

授课时间：7月1日上午10:00 - 12:00

7月2日上午10:00 - 12:00

7月3日上午10:00 - 12:00

7月4日上午10:00 - 12:00

课程题目：On Pesin's formula

课程摘要：In the lectures we first introduce measurable partitions into uncountably many subsets, and conditional measures and definition of entropy in the setting. The second part is about the proof of the Ruelle's inequality, that is, the metric entropy is bounded above by the integral of the sum of positive Lyapunov exponents.  The third part is the proof giving by Ledrappier and Strelcyn that the sufficient condition for Pesin entropy formula is that the measures have absolutely continuous conditinal measures on unstable manifolds. If time permits we will introduce the idea of the proof of the result of Ledrappier and Young that the absolute continuity on unstable manifolds is also the necessary condition for Pesin's fomula.