Dynamics of random selfmaps of surfaces with boundary

Details Dynamics of random selfmaps of surfaces with boundary Dynamics of random selfmaps of surfaces with boundary

2011-07-21

arxiv.org/abs/1107.4312v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

We use Wagner's algorithm to estimate the number of periodic points of certain selfmaps on compact surfaces with boundary. When counting according to homotopy classes, we can use the asymptotic density to measure the size of sets of selfmaps. In this sense, we show that "almost all" such selfmaps have periodic points of every period, and that in fact the number of periodic points of period n grows exponentially in n. We further discuss this exponential growth rate and the topological and fundamental-group entropies of these maps. Since our approach is via the Nielsen number, which is homotopy and homotopy-type invariant, our results hold for selfmaps of any space which has the homotopy type of a compact surface with boundary.

Affiliated with

Also associated with

No associations

Rating

Dynamics of random selfmaps of surfaces with boundary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamics of random selfmaps of surfaces with boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of random selfmaps of surfaces with boundary will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688173