天元讲堂（3.21，3.22）：Buzzi系统讲座
第一个报告信息
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. Ⅰ
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日09:30-10:30
报告地点 维格堂113
报告摘要 In the first talk, we will review some basic definitions and properties among differentiable ergodic theory. By a classical construction of Newhouse (1978), a homoclinic tangency can generate entropy through a C^1-perturbation. We show the outline of how this entropy can approximate the upperbound suggested by the Ruelle inequality.
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. ⅠI
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日10:30-11:30
报告地点 维格堂113
报告摘要 In the second talk, we will give some descriptions of the entropy map in the conservative settings, we find formulas for the topological entropy, deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism and furthermore we prove that these generic diffeomorphisms have no measure of maximum entropy.
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. ⅠII
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日11:30-12:30
报告地点 维格堂113
报告摘要 It has been known for some time that coexistence of infinitely many non-trivial homoclinic classes is locally generic. In this last talk, we will show that in the dissipative setting, the locally generic existence of infinitely many homoclinic classes with entropy bounded away from zero.
＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃
第二个报告信息
报告题目： Homoclinic classes of smooth surface diffeomorphisms. Ⅰ
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日09:30-10:30
报告地点 维格堂319
报告摘要 A celebrated theorem of Newhouse (1989) states that a C^infinity smooth diffeomorphism always has a measure maximizing the entropy. In his 1990 ICM address, Newhouse asked whether there are only finitely many ergodic such measures in the case of surfaces when the entropy is nonzero. We answer positively. In this talk, we will give some background and remarks of this question.
报告题目： Homoclinic classes of smooth surface diffeomorphisms. ⅠI
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日10:30-11:30
报告地点 维格堂319
报告摘要 In the second talk, we will show the strategy of the proof. Our proof relies on the analysis of homoclinic classes combining Sarig's symbolic coding, Yomdin's theory of local complexity for smooth maps and a version of the Sard lemma.
报告题目： Homoclinic classes of smooth surface diffeomorphisms. ⅠII
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日11:30-12:30
报告地点 维格堂319
报告摘要 As a consequence of the second, we will give a generalization of Smale's spectral decomposition and results for equilibrium measures and diffeomorphisms with finite regularity.
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. Ⅰ
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日09:30-10:30
报告地点 维格堂113
报告摘要 In the first talk, we will review some basic definitions and properties among differentiable ergodic theory. By a classical construction of Newhouse (1978), a homoclinic tangency can generate entropy through a C^1-perturbation. We show the outline of how this entropy can approximate the upperbound suggested by the Ruelle inequality.
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. ⅠI
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日10:30-11:30
报告地点 维格堂113
报告摘要 In the second talk, we will give some descriptions of the entropy map in the conservative settings, we find formulas for the topological entropy, deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism and furthermore we prove that these generic diffeomorphisms have no measure of maximum entropy.
报告题目： Entropy of C^1-diffeomorphisms without dominated splitting. ⅠII
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月21日11:30-12:30
报告地点 维格堂113
报告摘要 It has been known for some time that coexistence of infinitely many non-trivial homoclinic classes is locally generic. In this last talk, we will show that in the dissipative setting, the locally generic existence of infinitely many homoclinic classes with entropy bounded away from zero.
＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃
第二个报告信息
报告题目： Homoclinic classes of smooth surface diffeomorphisms. Ⅰ
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日09:30-10:30
报告地点 维格堂319
报告摘要 A celebrated theorem of Newhouse (1989) states that a C^infinity smooth diffeomorphism always has a measure maximizing the entropy. In his 1990 ICM address, Newhouse asked whether there are only finitely many ergodic such measures in the case of surfaces when the entropy is nonzero. We answer positively. In this talk, we will give some background and remarks of this question.
报告题目： Homoclinic classes of smooth surface diffeomorphisms. ⅠI
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日10:30-11:30
报告地点 维格堂319
报告摘要 In the second talk, we will show the strategy of the proof. Our proof relies on the analysis of homoclinic classes combining Sarig's symbolic coding, Yomdin's theory of local complexity for smooth maps and a version of the Sard lemma.
报告题目： Homoclinic classes of smooth surface diffeomorphisms. ⅠII
报告人 Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）
报告时间 2017年3月22日11:30-12:30
报告地点 维格堂319
报告摘要 As a consequence of the second, we will give a generalization of Smale's spectral decomposition and results for equilibrium measures and diffeomorphisms with finite regularity.