Dynamics of commuting homeomorphisms of chainable continua

Christopher Mouron

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Displaying similar documents to “Dynamics of commuting homeomorphisms of chainable continua”

On indecomposability and composants of chaotic continua

Hisao Kato (1996)

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A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that $d (f^{n} (x), f^{n} (y)) > c$ . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that $d i a m i f^{n} (A) > c$ . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua...

The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites

Enhui Shi, Suhua Wang (2009)

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It is shown that each expansive group action on a Peano continuum having a free dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, it is shown that each Peano continuum having a free dendrite admits no expansive nilpotent group actions.

A chainable continuum not homeomorphic to an inverse limit on [0, 1] with only one bonding map

Dorothy S. Marsh (1980)

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Continua which cannot be mapped onto any nonplaner circle-like continuum

George W. Henderson (1971)

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The solenoids are the only circle-like continua that admit expansive homeomorphisms

Christopher Mouron (2009)

Fundamenta Mathematicae

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A homeomorphism h:X → X of a compactum X is expansive provided that for some fixed c > 0 and any distinct x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a circle-like continuum that admits an expansive homeomorphism, then X is homeomorphic to a solenoid.

On Applications of Bing-Krasinkiewicz-Lelek Maps

Eiichi Matsuhashi (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.

Chainable continua and homeomorphisms of the plane onto itself

Mirosław Sobolewski (1984)

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On composants of solenoids.

de Man, Ronald (1995)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Fully closed maps and non-metrizable higher-dimensional Anderson-Choquet continua

Jerzy Krzempek (2010)

Colloquium Mathematicae

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Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's rigid continua. Certain theorems on dimension-lowering maps are proved for inductive dimensions and fully closed maps from spaces that need not be hereditarily normal, and some of the examples of continua we construct have non-coinciding dimensions.

Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets

Chris Good, Brian E. Raines (2006)

Fundamenta Mathematicae

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We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.

Monotone images of $w$ -sets and hereditarily weakly confluent images of continua.

Hatch, Jonathan, Stanojević, Č.V. (2003)

Publications de l'Institut Mathématique. Nouvelle Série

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ω-Limit sets for triangular mappings

Victor Jiménez López, Jaroslav Smítal (2001)

Fundamenta Mathematicae

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In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua...

Expansive homeomorphisms and indecomposability

Hisao Kuto (1991)

Fundamenta Mathematicae

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No arc-connected treelike continuum is the 2-to-1 image of a continuum

Jo Heath, Van C. Nall (2003)

Fundamenta Mathematicae

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In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

An Exactly Two-to-One Map from an Indecomposable Chainable Continuum

Jerzy Krzempek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.

On Cosserat continua

S. Drobot (1971)

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On topological sequence entropy and chaotic maps on inverse limit spaces.

Canovas, J.S. (1999)

Acta Mathematica Universitatis Comenianae. New Series

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Whitney properties

J. Krasinkiewicz, Sam Nadler (1978)

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A distributionally chaotic triangular map with zero sequence topological entropy.

Forti, G.L., Paganoni, L. (1998)

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