报告人 王晓东（上海交通大学）
报告时间 2016年12月5日10:00-12:00
报告地点 维格堂319
报告摘要 We prove the “star” conjecture restricted to homoclinic classes. To be precise, for C1-generic diffeomorphisms, if the periodic orbits contained in a homoclinic class H(p) have all their Lyapunov exponents bounded away from 0, then H(p) must be (uni- formly) hyperbolic. This gives a way to characterize lack of hyperbolicity of homoclinic classes through the existence of “weak” periodic orbits. The main difficulty to be “re- stricted” is that the homoclinic class H(p) is not known isolated in advance. Hence the “weak” periodic orbits created by perturbations near the homoclinic class have to be guaranteed strictly inside the homoclinic class. We construct in the proof several perturbations which are not simple applications of the connecting lemmas.