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Average shadowing properties on compact metric spaces

Yong Zhang|박종진
대한수학회 (The Korean Mathematical Society)|2006.04|대한수학회논문집 (Communications of the KMS)|제21권 제2호|pp. 355-361

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참고문헌

주제분류수학

초록

Abstract

We prove that if a continuous surjective map f on a compactmetric space X has the average shadowing property, then everypoint x is chain recurrent.We also show that if a homeomorphism f has more than two fixed points on S^1,then f does not satisfy the average shadowing property.Moreover, we construct a homeomorphism on a circle which satisfies the shadowing propertybut not the average shadowing property.This shows that the converse of the theorem 1.1 in [6] is not true.

참고문헌 (6)

  1. "Equilibrium states and the ergodic theory of axiom A diffeomorphims}", pp.68~ (1975)
  2. "Metric properties of epsilon-trajectory of dynamical systems with stochastic behavior", pp.365~ (1988)
  3. "Small perturbations of chaotic dynamical systems", pp.1~ (1989)
  4. "Pseudo orbit tracing property and limit shadowing property on a circle" (2000)
  5. "Diffeomorphisms with the average-shadowing property on two dimensional closed manifold" (2000)
  6. "On the average-shadowing property" (2001)

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