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\(N\)-expansive flows. (English) Zbl 1484.37040

Summary: We define the concept of \(N\)-expansivity for flows and extend some of the results already established for discrete dynamics and for \(CW\)-expansive flows. We show examples of \(N\)-expansive flows but not expansive, and examples of CW-expansive flows but not \(N\)-expansive for any natural number \(N\). We also define Komuro \(N\)-expansivity and prove that on compact surfaces it implies Komuro expansivity.

MSC:

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C10 Dynamics induced by flows and semiflows
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37B40 Topological entropy
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References:

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