Displaying similar documents to “Ordered K-theoryand minimal symbolic dynamical systems”

Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows

T. Downarowicz, Y. Lacroix (1998)

Studia Mathematica

Similarity:

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...

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

Wojciech Bulatek, Jan Kwiatkowski (1990)

Publicacions Matemàtiques

Similarity:

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.

Toeplitz flows with pure point spectrum

A. Iwanik (1996)

Studia Mathematica

Similarity:

We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.

Some constructions of strictly ergodic non-regular Toeplitz flows

A. Iwanik, Y. Lacroix (1994)

Studia Mathematica

Similarity:

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

Similarity:

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.