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KCI등재 학술저널

TOPOLOGICAL ENTROPY OF EXPANSIVE FLOW ON TVS-CONE METRIC SPACES

DOI : 10.14403/jcms.2021.34.3.259
  • 4

We shall study the following. Let phi be an expansive flow on a compact TVS-cone metric space (X,d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that limsup {1over t} log v(t) le h(phi), where v(t) denotes the number of closed orbits of phi with a period tau in [0,t] and h(phi) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space

1. Introduction and Preliminaries

2. Some equivalent definitions of expansive flows

3. Conjugate invariance

4. Topological entropy of expansive flows

References

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