Persistence of heterodimensional cycles

发布时间：2024-05-27 作者：浏览次数：

Speaker:	Dongchen Li	DateTime:	2024年5月31日（周五）晚上20:00-21:00
Brief Introduction to Speaker: Dongchen Li，Imperial College London, 研究员		Place:	腾讯会议：763-648-180
Abstract:The existence of heterodimensional cycles is believed to be one of two basic mechanisms leading to non-hyperbolicity, where the other one is the existence of homoclinic tangencies. We show that any $C^r$ ($r=2,\ldots,\infty,\omega$) system having a heterodimensional cycle can be approximated in the $C^r$ topology by systems having robust heterodimensional cycles. This implies a heterodimensional counterpart to the well-known Newhouse theorem that every homoclinic tangency is C^r close to robust homoclinic tangencies. The result is based on the observation that arithmetic properties of moduli of topological conjugacy of systems with heterodimensional cycles determine the emergence of Bonatti-D\'iaz blenders.