Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778064 | Topology and its Applications | 2017 | 11 Pages |
Abstract
For continuous maps of compact metric spaces f:XâX and g:YâY and for various notions of topological recurrence, we study the relationship between recurrence for f and g and recurrence for the product map fÃg:XÃYâXÃY. For the generalized recurrent set GR, we see that GR(fÃg)=GR(f)ÃGR(g). For the nonwandering set NW, we see that NW(fÃg)âNW(f)ÃNW(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
Authors
Jim Wiseman,