Displaying similar documents to “Toeplitz flows with pure point spectrum”

Some constructions of strictly ergodic non-regular Toeplitz flows

A. Iwanik, Y. Lacroix (1994)

Studia Mathematica

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We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.

A non-regular Toeplitz flow with preset pure point spectrum

T. Downarowicz, Y. Lacroix (1996)

Studia Mathematica

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Given an arbitrary countable subgroup σ 0 of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to σ 0 . For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

The topological centralizers of Toeplitz flows and their Z-extensions.

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.

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

A criterion for Toeplitz flows to be topologically isomorphic and applications

T. Downarowicz, J. Kwiatkowski, Y. Lacroix (1995)

Colloquium Mathematicae

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A dynamical system is said to be coalescent if its only endomorphisms are automorphisms. The question whether there exist coalescent ergodic dynamical systems with positive entropy has not been solved so far and it seems to be difficult. The analogous problem in topological dynamics has been solved by Walters ([W]). His example, however, is not minimal. In [B-K2], a class of strictly ergodic (hence minimal) Toeplitz flows is presented, which have positive entropy and trivial topological...