Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits

Details Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits

1999-02-26

arxiv.org/abs/math/9902159v1

Mathematics

Dynamical Systems

12 pages, 7 postscript figures

Scientific paper

10.1007/s002200050811

Consider a compact manifold M of dimension at least 2 and the space of C^r-smooth diffeomorphisms Diff^r(M). The classical Artin-Mazur theorem says that for a dense subset D of Diff^r(M) the number of isolated periodic points grows at most exponentially fast (call it the A-M property). We extend this result and prove that diffeomorphisms having only hyperbolic periodic points with the A-M property are dense in Diff^r(M). Our proof of this result is much simpler than the original proof of Artin-Mazur. The second main result is that the A-M property is not (Baire) generic. Moreover, in a Newhouse domain ${\cal N} \subset Diff^r(M)$, an arbitrary quick growth of the number of periodic points holds on a residual set. This result follows from a theorem of Gonchenko-Shilnikov-Turaev, a detailed proof of which is also presented.

Affiliated with

Also associated with

No associations

Rating

Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits 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 Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368707