动力系统讨论班——STAR FLOW WITH SINGULARITIES OF DIFFERENT INDICES
主 题: 动力系统讨论班——STAR FLOW WITH SINGULARITIES OF DIFFERENT INDICES
报告人: Adriana da Luz (Univ. Bourgogne and CMAT)
时 间: 2016-09-29 15：10-17：00
地 点: 理科一号楼1418
A vector field X is called a star flow if every periodic orbit of any vector field C1-close to X is hyperbolic.It is known that an isolated chain recurrent class of a star flow X on a 3 or 4 manifold are either hyperbolic, or singular hyperbolic (Morales, pacifico Pujals for 3 manifolds and Ming Li, Shaobo Gan and Lan Wen on 4-manifolds). Moreover, it was recently proven by Yi Shi Shaobo Gan and Lan Wen for every chain recurrent class C of X a star flow X, if all singularities in C have the same index, then the chain recurrent set of X is singular hyperbolic. We present here a non empty open set of star flows on a 5-manifold for which two singular points of different indices belong (robustly) to the same chain recurrence class. This prevent the class to be singular hyperbolic. We also present a weak form of hyperbonicity (called multisingular hyperbolic) which makes compatible the hyperbolic structures of regular orbits together with the one of singularities of index 2 and 3. This is a joint work with Christian Bonatti.