Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Kwapisz, Jaros law

doi:10.4064/fm168-3-3

Cited by 16 publications

(22 citation statements)

References 20 publications

(28 reference statements)

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“…This result was proved by Kwapisz [30]. The result has been accepted and used, but this is the first correct proof in the literature.…”

Section: The Knaster Continuummentioning

confidence: 77%

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Attractors and inverse limits

Keesling

2008

Rev. R. Acad. Cien. Serie A. Mat.

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This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram's Conjecture. Some motivation is given for the study of such inverse limits. Atractores y límites inversosResumen. Este artículo expone algunos resultados recientes sobre límites inversos de aplicaciones tienda. La exposición se concentra en la Conjetura de Ingram. Se presentan tambien algunas motivaciones para el estudio de tales límites inversos.

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“…This result was proved by Kwapisz [30]. The result has been accepted and used, but this is the first correct proof in the literature.…”

Section: The Knaster Continuummentioning

confidence: 77%

“…Each homeomorphism h of a solenoid Σ α has the same topological entropy as a certain automorphism α ∈ Aut(Σ α ) associated uniquely with h. This result was recently proved by Kwapisz [30]. The topological entropy of automorphisms of solenoids can be calculated using techniques determined by Abramov [1].…”

Section: The Solenoidmentioning

confidence: 85%

Attractors and inverse limits

Keesling

2008

Rev. R. Acad. Cien. Serie A. Mat.

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“…Let (Φ t ) t∈R be the suspension flow on X over the 2-adic odometer h. Let us represent the 2-adic solenoid as X = (Λ 2 × R)/ ≈, where Λ 2 is the 2-adic Cantor set, seen as the group of 2-adic integers, and (c, x) ≈ (c , x ) if and only if h(c) = c and x + 1 = x . By [24] X admits an orientation reversing algebraic homeomorphism A induced by A :…”

Section: Almost Slovak Spaces That Do Not Admit Minimal Noninvertiblementioning

confidence: 99%

On Rigid Minimal Spaces

2020

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A compact space X is said to be minimal if there exists a map f : X → X such that the forward orbit of any point is dense in X. We consider rigid minimal spaces, motivated by recent results of Downarowicz, Snoha, and Tywoniuk [J. Dyn. Diff. Eq., 2016] on spaces with cyclic group of homeomorphisms generated by a minimal homeomorphism, and results of the first author, Clark and Oprocha [Adv. Math., 2018] on spaces in which the square of every homeomorphism is a power of the same minimal homeomorphism. We show that the two classes do not coincide, which gives rise to a new class of spaces that admit minimal homeomorphisms, but no minimal maps. We modify the latter class of examples to show for the first time existence of minimal spaces with degenerate homeomorphism groups. Finally, we give a method of constructing decomposable compact and connected spaces with cyclic group of homeomorphisms, generated by a minimal homeomorphism, answering a question in Downarowicz et al.

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“…The space of orientation-preserving homeomorphisms isotopic to the identity of S is denoted by Homeo + (S), and the space containing all the liftings of homeomorphisms in Homeo + (S) will be denoted by Homeo + (S). By [Kwa2] we have a complete description of the homeomorphisms in Homeo + (S).…”

Section: Homeomorphisms That Are Isotopic To the Identitymentioning

confidence: 99%