Abstract
Fathi and Pageault have recently shown a connection between Auslander’s generalized recurrent set$\text{GR}(f)$and Easton’s strong chain recurrent set. We study$\text{GR}(f)$by examining that connection in more detail, as well as connections with other notions of recurrence. We give equivalent definitions that do not refer to a metric. In particular, we show that$\text{GR}(f^{k})=\text{GR}(f)$for any$k>0$, and give a characterization of maps for which the generalized recurrent set is different from the ordinary chain recurrent set.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference27 articles.
1. Generalized recurrence in dynamical systems;Auslander;Contrib. Differ. Equ.,1964
2. Dynamics of topologically generic homeomorphisms;Akin;Mem. Amer. Math. Soc.,2003
3. The closing lemma for generalized recurrence in the plane
4. The Derivative of Minkowski's ?(x) Function
5. Some Aspects of Stability for Semigroup Actions and Control Systems
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献