Chaotic group actions on manifolds

Naolekar, Aniruddha C.; Sankaran, Parameswaran

doi:10.1016/s0166-8641(99)00113-3

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Introduction2

Remark 121

Nt1

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2003

2014

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Cited by 16 publications

(4 citation statements)

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“…For more results about chaotic group actions see [Cairns & Kolganova, 1996] and [Naolekar & Sankaran, 2000].…”

Section: Remark 12mentioning

confidence: 99%

Topological Transitivity and Chaos of Group Actions on Dendrites

Wang¹,

Shi²,

Zhou³

et al. 2009

Int. J. Bifurcation Chaos

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“…For more results about chaotic group actions see [Cairns & Kolganova, 1996] and [Naolekar & Sankaran, 2000].…”

Section: Remark 12mentioning

confidence: 99%

Topological Transitivity and Chaos of Group Actions on Dendrites

Wang¹,

Shi²,

Zhou³

et al. 2009

Int. J. Bifurcation Chaos

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“…Proof. Using the idea in [ 1 ] or the method used in [2], we can easily construct a chaotic Z × Shi Enhui et al…”

Section: Ntmentioning

confidence: 99%

“…This paper is the sequel to [ 1,2]. Cairns et al [t] introduced the notion of a chaotic group action as a generalization of chaotic dynamical systems(see definition below).…”

Section: § 1 Introductionmentioning

confidence: 99%

Chaotic group actions

Shi

Zhou

You-cheng

2003

Appl. Math. Chin. Univ.

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It is proved that there is no chaotic group actions on any topological space with free arc. In this paper the chaotic actions of the group like G x F,where F is a finite group~are studied. In particular,under a suitable assumption, if F is a cyclic group, then the topological space which admits a chaotic action of Z x F must admit a chaotic homeomorphism. A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.

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“…In [6], Naolekar and Sankaran conjectured that on Euclidean space, there are no chaotic group actions via compactly supported homeomorphisms. They established this in several cases, including the cases of finitely generated groups and solvable groups.…”

Section: Introductionmentioning

confidence: 99%