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

Studia Mathematica (1998)

- Volume: 130, Issue: 2, page 149-170
- ISSN: 0039-3223

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topDownarowicz, T., and Lacroix, Y.. "Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows." Studia Mathematica 130.2 (1998): 149-170. <http://eudml.org/doc/216549>.

@article{Downarowicz1998,

abstract = {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 ergodic toeplitz flow.},

author = {Downarowicz, T., Lacroix, Y.},

journal = {Studia Mathematica},

keywords = {almost 1-1 extension; invariant measure; isomorphism; Toeplitz flow; measure isomorphism; topological extension; subshift; almost extension; ergodic Toeplitz flow},

language = {eng},

number = {2},

pages = {149-170},

title = {Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows},

url = {http://eudml.org/doc/216549},

volume = {130},

year = {1998},

}

TY - JOUR

AU - Downarowicz, T.

AU - Lacroix, Y.

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

JO - Studia Mathematica

PY - 1998

VL - 130

IS - 2

SP - 149

EP - 170

AB - 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 ergodic toeplitz flow.

LA - eng

KW - almost 1-1 extension; invariant measure; isomorphism; Toeplitz flow; measure isomorphism; topological extension; subshift; almost extension; ergodic Toeplitz flow

UR - http://eudml.org/doc/216549

ER -

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