• Title/Summary/Keyword: h-expansive flow

Search Result 1, Processing Time 0.014 seconds

TOPOLOGICAL ENTROPY OF EXPANSIVE FLOW ON TVS-CONE METRIC SPACES

  • Lee, Kyung Bok
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.34 no.3
    • /
    • pp.259-269
    • /
    • 2021
  • We shall study the following. Let 𝜙 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 lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) 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 [?].