On the existence of attractors

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dc.creatorBonatti, Christian
dc.creatorLi, Ming
dc.creatorYang, Dawei
dc.date2009-04-28
dc.date.accessioned2026-07-07T13:09:25Z
dc.date.available2026-07-07T13:09:25Z
dc.descriptionOn 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0904.4393
dc.identifierhttp://arxiv.org/abs/0904.4393
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228729
dc.subjectDynamical Systems
dc.subject37C05, 37C20, 37C25, 37C29, 37D30
dc.titleOn the existence of attractors
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