A generalization of expansivity
By Carlos Arnoldo Morales. 2011
78 citations recorded by the source corpus.
We study dynamical systems for which at most $n$ orbits can accompany a given arbitrary orbit. For simplicity we call them $n$-expansive (or positively $n$-expansive if positive orbits are considered instead). We prove that these systems can satisfy properties of expansive systems or not. For instance, unlike positively expansive maps [3], positively $n$-expansive homeomorphisms may exist on certain infinite compact metric spaces. We also prove that a map (resp. bijective map) is positively $n$-expansive (resp. $n$-expansive) if and only if it is so outside finitely many points. Finally, we prove that a homeomorphism on a compact metric space is $n$-expansive if and only if it is so outside finitely many orbits. These last resuls extends previous ones for expansive systems [2],[11],[12].
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9cb2c69464294b147aa8f65015a3b0bfc669e76f
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- N-expansive homeomorphisms with the shadowing property (2016, background): “A generalization of the expansiveness property that has been given attention recently is the n -expansive property (see [3], [4], [10], [12]).”