# Spectrum of multidimensional dynamical systems with positive entropy

Studia Mathematica (1994)

- Volume: 108, Issue: 1, page 77-85
- ISSN: 0039-3223

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topKamiński, B., and Liardet, P.. "Spectrum of multidimensional dynamical systems with positive entropy." Studia Mathematica 108.1 (1994): 77-85. <http://eudml.org/doc/216042>.

@article{Kamiński1994,

abstract = {Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^d$-action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^∞$-actions. Next, using its relative version, we extend to $ℤ^∞$-actions some other general results connecting spectrum and entropy.},

author = {Kamiński, B., Liardet, P.},

journal = {Studia Mathematica},

keywords = {positive entropy; Kolmogorov automorphism; Lebesgue spectrum; -actions; countable Abelian group},

language = {eng},

number = {1},

pages = {77-85},

title = {Spectrum of multidimensional dynamical systems with positive entropy},

url = {http://eudml.org/doc/216042},

volume = {108},

year = {1994},

}

TY - JOUR

AU - Kamiński, B.

AU - Liardet, P.

TI - Spectrum of multidimensional dynamical systems with positive entropy

JO - Studia Mathematica

PY - 1994

VL - 108

IS - 1

SP - 77

EP - 85

AB - Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov $ℤ^d$-action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to $ℤ^∞$-actions. Next, using its relative version, we extend to $ℤ^∞$-actions some other general results connecting spectrum and entropy.

LA - eng

KW - positive entropy; Kolmogorov automorphism; Lebesgue spectrum; -actions; countable Abelian group

UR - http://eudml.org/doc/216042

ER -

## References

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