Syndetic sensitivity in semiflows

Miller, Alica; Money, Chad

doi:10.1016/j.topol.2015.09.008

Cited by 19 publications

(7 citation statements)

References 7 publications

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“…The next proposition is from our paper [6], written jointly with C. Money. We include the proof for the sake of completeness.…”

Section: Resultsmentioning

confidence: 99%

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Devaney's chaos and eventual sensitivity

Miller¹

2019

Preprint

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We give an equivalent definition of Devaney chaotic semiflow in terms of eventual sensitivity, the notion recently introduced by C. Good, R. Leek, and J. Mitchell. As a consequence, we prove a version of Auslander-Yorke dichotomy for the case of not necessarily compact phase spaces. Finally, we raise some questions about the relation between Devaney chaoticity and the notion of topological sensitivity, which was recently introduced by C. Good and C. Macías.

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“…The next proposition is from our paper [6], written jointly with C. Money. We include the proof for the sake of completeness.…”

Section: Resultsmentioning

confidence: 99%

“…The paper is self-contained, i.e., all the notions used in the paper are defined in it. The reader can also consult the standard reference [7] and papers [5,6] for additional information.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Devaney's chaos and eventual sensitivity

Miller¹

2019

Preprint

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“…Proof Follows from Propositions 6.6 and 6.4. [11]. It is sensitive and so (T, X × X) is also sensitive according to Proposition 7.1.…”

Section: (Dpp) On the Productmentioning

confidence: 93%

“…Equivalently, a semiflow is Devaney chaotic if it is (TT), has (DPP), and is (S) (see the papers [1,5,11], where it is shown that, when (NMIN) holds, (S) follows from (TT)+(DPP)).…”

Section: Devaney Chaos On the Product Definition 81 A Semiflow (T Xmentioning

confidence: 99%

Chaos-related properties on the product of semiflows

Miller¹,

Money²

2017

Turk J Math

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In this paper we generalize some results about the chaos-related properties on the product of two semiflows, which appeared in the literature in the last few years, to the case of the most general possible acting monoids. In order to do that we introduce some new notions, namely the notions of a directional, psp and sip monoid, and the notion of a strongly transitive semiflow. In particular, we obtain a sufficient condition for the Devaney chaoticity of a product, which works for the (very large) class of the psp acting monoids.

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“…Recently, Miller and Money [11] proved that a non-minimal syndetically transitive semiflow is syndetically sensitive, generalizing some results in [1,3,14,16]. Then, they [12] generalized some results on chaotic properties of cascades to the product of semiflows and asked the following question.…”

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confidence: 95%