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Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Jarosław Kwapisz — 2001

Fundamenta Mathematicae

We describe the homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological entropy and that they are actually semi-conjugate to an algebraic homeomorphism in the case when the entropy is positive.

Topological friction in aperiodic minimal $ℝ^{m}$ -actions

Jarosław Kwapisz — 2010

Fundamenta Mathematicae

For a continuous map f preserving orbits of an aperiodic $ℝ^{m}$ -action on a compact space, its displacement function assigns to x the “time” $t \in ℝ^{m}$ it takes to move x to f(x). We show that this function is continuous if the action is minimal. In particular, f is homotopic to the identity along the orbits of the action.

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $β$ -shifts

Veronica Baker; Marcy Barge; Jaroslaw Kwapisz — 2006

Annales de l’institut Fourier

This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.

Weighted norms and Volterra integral equations in $L^{p}$ spaces.

Kwapisz, Jaroslaw — 1991

Journal of Applied Mathematics and Stochastic Analysis

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Currently displaying 1 – 4 of 4

Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Topological friction in aperiodic minimal $ℝ^{m}$ -actions

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $β$ -shifts

Weighted norms and Volterra integral equations in $L^{p}$ spaces.

Advanced Search

Formula preview

Currently displaying 1 – 4 of 4

Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Topological friction in aperiodic minimal ℝ m -actions

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Weighted norms and Volterra integral equations in L p spaces.

Topological friction in aperiodic minimal $ℝ^{m}$ -actions

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $β$ -shifts

Weighted norms and Volterra integral equations in $L^{p}$ spaces.