报告题目： The relationship between Lyapunov exponents and entropies I (part 1)


报告人 谢践生（复旦大学）


报告时间 2017年7月18日12:30-13:30

报告地点  维格堂319

报告摘要  In this talk we discuss the martingale techniques in proving Shannon’s theorem. We will present an important estimation in a general setting which is frequently exploited in Ledrappier-Young Theory. 


报告题目：The relationship between Lyapunov exponents and entropies II (part 2)

报告人 谢践生（复旦大学）


报告时间 2017年7月18日13:30-14:30

报告地点  维格堂319

报告摘要  In this talk we introduce the so-called Lyapunov charts based on the famous Oseledec’s Multiplicative Ergdoci Theorem. With the help of Lyapunov charts, the strong stabe/unstable manifolds are discussed. These are the geometrical preliminaries for the Ledrappier-Young Theory. We construct several special partitions which would be useful in proving Ledrappier-Young Theory. The so-called Kac’s formula plays an important role in the construction.

报告题目：The relationship between Lyapunov exponents and entropies III (part 3)

报告人 谢践生（复旦大学）


报告时间 2017年7月18日14:30-15:30

报告地点  维格堂319

报告摘要 In this talk we combine all the preceding preliminaries and techniques and give a proof of Ledrappier-Young entropy formula. In view of this formula, SRB property holds true if and only if Pesin’s entropy formula holds. This is also a pre-step for the so-called Eckmann-Ruelle conjecture.