Aperiodic chain recurrence classes of C1-generic diffeomorphisms

• 成果类型: Article; Early Access
• 署名作者: Bonatti, Christian; Shinohara, Katsutoshi
• 署名单位: Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Hitotsubashi University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01290-0
• 发表日期: 2024
• 关键词: structural stability; DYNAMICAL-SYSTEMS

摘要

We consider the space of C-1-diffeomorphims of a three dimensional closed manifold equipped with the C-1-topology. It is known that there are open sets in which C-1-generic diffeomorphisms display uncountably many chain recurrence classes, while only countably many of them may contain periodic orbits. The classes without periodic orbits, called aperiodic classes, are the main subject of this paper. The aim of the paper is to show that aperiodic classes of C-1-generic diffeomorphisms can exhibit a variety of topological properties. More specifically, there are C-1-generic diffeomorphisms with (1) minimal expansive aperiodic classes, (2) minimal but non-uniquely ergodic aperiodic classes, (3) transitive but non-minimal aperiodic classes, (4) non-transitive, uniquely ergodic aperiodic classes.