2017
DOI: 10.22436/jnsa.010.09.34
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Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows

Abstract: In this paper, for a continuous semi-flow θ on a compact metric space E with the asymptotic average-shadowing property (AASP), we show that if the almost periodic points of θ are dense in E then θ is multi-sensitive and syndetically sensitive. Also, we show that if θ is a Lyapunov stable semi-flow with the AASP, then the space E is trivial. Consequently, a Lyapunov stable semi-flow with the AASP is minimal. Furthermore, we prove that for a syndetically transitive continuous semi-flow on a compact metric space,… Show more

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“…We thus generalized Moothathu's first comment to the case of general semiflows and showed that his second comment does not hold in general semiflows. Let us also mention that multi-sensitivity for continuous semiflows was discussed in [5].…”
Section: Introductionmentioning
confidence: 99%
“…We thus generalized Moothathu's first comment to the case of general semiflows and showed that his second comment does not hold in general semiflows. Let us also mention that multi-sensitivity for continuous semiflows was discussed in [5].…”
Section: Introductionmentioning
confidence: 99%