Article ID Journal Published Year Pages File Type
5778064 Topology and its Applications 2017 11 Pages PDF
Abstract
For continuous maps of compact metric spaces f:X→X and g:Y→Y and for various notions of topological recurrence, we study the relationship between recurrence for f and g and recurrence for the product map f×g:X×Y→X×Y. For the generalized recurrent set GR, we see that GR(f×g)=GR(f)×GR(g). For the nonwandering set NW, we see that NW(f×g)⊂NW(f)×NW(g) and give necessary and sufficient conditions on f for equality for every g. We also consider product recurrence for the chain recurrent set, the strong chain recurrent set, and the Mañé set.
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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