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A note on generic chaos

100%

Liao G.

Annales Polonici Mathematici

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1994

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tom 59

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nr 2

99-105

EN

We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.

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The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos

51%

Wang L., Liao G., Chen Z., Duan X.

Annales Polonici Mathematici

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2003

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tom 82

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nr 3

265-272

EN

We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

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Recurrent point set of the shift on Σ and strong chaos

51%

Wang L., Liao G., Yang Y.

Annales Polonici Mathematici

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2002

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tom 78

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nr 2

123-130

EN

Let (Σ,ϱ) be the one-sided symbolic space (with two symbols), and let σ be the shift on Σ. We use A(·), R(·) to denote the set of almost periodic points and the set of recurrent points respectively. In this paper, we prove that the one-sided shift is strongly chaotic (in the sense of Schweizer-Smítal) and there is a strongly chaotic set 𝒥 satisfying 𝒥 ⊂ R(σ)-A(σ).

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Liao G.

2 Wang L.

1 Chen Z.

1 Duan X.

1 Yang Y.

1 2003

1 2002

1 1994

A note on generic chaos

The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos

Recurrent point set of the shift on Σ and strong chaos