On the existence of attractors

Details On the existence of attractors On the existence of attractors

2009-04-28

arxiv.org/abs/0904.4393v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

On every compact 3-manifold, we build a non-empty open set $\cU$ of $\Diff^1(M)$ such that, for every $r\geq 1$, every $C^r$-generic diffeomorphism $f\in\cU\cap \Diff^r(M)$ has no topological attractors. On higher dimensional manifolds, one may require that $f$ has neither topological attractors nor topological repellers. Our examples have finitely many quasi attractors. For flows, we may require that these quasi attractors contain singular points. Finally we discuss alternative definitions of attractors which may be better adapted to generic dynamics.

Affiliated with

Also associated with

No associations

Rating

On the existence of attractors 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 On the existence of attractors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the existence of attractors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-713077