### The centralizer of Morse shifts

Mariusz Lemanczyk (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Mariusz Lemanczyk (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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J. Kwiatkowski (1986)

Studia Mathematica

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Roman Srzednicki (1999)

Banach Center Publications

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The Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the...

Wojciech Bulatek, Jan Kwiatkowski (1990)

Publicacions Matemàtiques

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The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z-extensions are described. Such Toeplitz flows are topologically coalescent. If {q, q, ...} is a set of all except at least one prime numbers and I, I, ... are positive integers then the direct sum ⊕ Z ⊕ Z can be the topological centralizer of a Toeplitz flow.

Jan Kwiatkowski, Andrzej Sikorski (1987)

Bulletin de la Société Mathématique de France

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T. Downarowicz, Y. Lacroix (1998)

Studia Mathematica

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Let $(Z,{T}_{Z})$ be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of $(Z,{T}_{Z})$ is Borel isomorphic to an almost 1-1 extension of $(Z,{T}_{Z})$. Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly...

Christopher McCord (1999)

Banach Center Publications

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Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy...

J. Kwiatkowski (1982)

Studia Mathematica

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Mogollon, Ramon (1980)

International Journal of Mathematics and Mathematical Sciences

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