16:00 - 17:30, October 23, 2024 (Wednesday) Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Persistence of Heterodimensional Cycles Dongchen Li (Imperial College London)
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 system having a heterodimensional cycle can be approximated in the topology by systems having robust heterodimensional cycles. This implies a heterodimensional counterpart to the well-known Newhouse theorem that every homoclinic tangency is 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-Díaz blenders.
