Skew-Product Dynamical Systems, Ellis Groups and Topological Centre

Jabbari, Ali; Vishki, Hamid Reza Ebrahimi

doi:10.1017/s0004972708001172

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…This answers the problem posed in Remark 6.4 (e) by Jabbari and Vishki [8]. Notice that the previous lemma implies that each element σ ∈ Λ(Σ) determines a unique element (n, u) of the space Z × T. Let Ψ : Λ(Σ) → Z × T be defined by Ψ(σ) = (n, u).…”

Section: Remarksupporting

confidence: 67%

Ellis Group and the Topological Center of the Flow Generated by the Map $${n \mapsto {\lambda^{n}}^{k}}$$

Jabbari

Namioka

2010

Milan J. Math.

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For each natural number k and each irrational member λ of the unit circle, it is proved that the shift-orbit closure X f of the function f (n) = λ n k is homeomorphic to a k-torus. Using this homeomorphism, we investigate the Ellis group and its topological center of the dynamical system (X f , U), where U is the shift operator on l ∞ (Z). Finally, it is shown that the topological center of the spectrum of the Weyl algebra is the image of Z in the spectrum .Mathematics Subject Classification (2010). 43A60.

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Section: Remarksupporting

confidence: 67%

Ellis Group and the Topological Center of the Flow Generated by the Map $${n \mapsto {\lambda^{n}}^{k}}$$

Jabbari

Namioka

2010

Milan J. Math.

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“…As a final comment, we note that it would be interesting to see if the technics of this section could be adapted to variants of Furstenberg transformations (such as the ones studied in [28], [35] or [43]).…”

Section: Furstenberg Transformationsmentioning

confidence: 99%

Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

Aldecoa¹

2014

Ergod. Th. Dynam. Sys.

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We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an illustration, we consider time changes of horocycle flows, skew products over translations and Furstenberg transformations. For time changes of horocycle flows, we obtain absolute continuity under assumptions weaker than the ones to be found in the literature.

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“…Throughout this paper, (T k , T ) denotes the Hahn-type skew product dynamical system (see [4]) defined as follows:…”

Section: Characterizing X F With a Torus Dynamical Systemmentioning

confidence: 99%

Skew-Product Dynamical Systems, Ellis Groups and Topological Centre

Cited by 8 publications

References 16 publications

Ellis Group and the Topological Center of the Flow Generated by the Map $${n \mapsto {\lambda^{n}}^{k}}$$

Ellis Group and the Topological Center of the Flow Generated by the Map $${n \mapsto {\lambda^{n}}^{k}}$$

Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

On a problem concerning the Banach algebra generated by the maps $n\mapsto\lambda^{\binom{n}{k}}$

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