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Invariant measures for interval translations and some other piecewise continuous maps. / Kryzhevich, Sergey .

в: Mathematical Modelling of Natural Phenomena, Том 15, 15, 12.03.2020.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Kryzhevich, S 2020, 'Invariant measures for interval translations and some other piecewise continuous maps', Mathematical Modelling of Natural Phenomena, Том. 15, 15. https://doi.org/10.1051/mmnp/2019041

APA

Kryzhevich, S. (2020). Invariant measures for interval translations and some other piecewise continuous maps. Mathematical Modelling of Natural Phenomena, 15, [15]. https://doi.org/10.1051/mmnp/2019041

Vancouver

Kryzhevich S. Invariant measures for interval translations and some other piecewise continuous maps. Mathematical Modelling of Natural Phenomena. 2020 Март 12;15. 15. https://doi.org/10.1051/mmnp/2019041

Author

Kryzhevich, Sergey . / Invariant measures for interval translations and some other piecewise continuous maps. в: Mathematical Modelling of Natural Phenomena. 2020 ; Том 15.

BibTeX

@article{de50a89d0c60409cafb3550482c7fb34,
title = "Invariant measures for interval translations and some other piecewise continuous maps",
abstract = "We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.",
keywords = "Krylov-Bogolybov theorem, invariant measures, periodic points, piecewise continuous maps, piecewise isometries, interval translation maps, Periodic points, Interval translation maps, Invariant measures, Piecewise isometries, Piecewise continuous maps",
author = "Sergey Kryzhevich",
note = "Publisher Copyright: {\textcopyright} EDP Sciences, 2020.",
year = "2020",
month = mar,
day = "12",
doi = "10.1051/mmnp/2019041",
language = "English",
volume = "15",
journal = "Mathematical Modelling of Natural Phenomena",
issn = "0973-5348",
publisher = "EDP Sciences",

}

RIS

TY - JOUR

T1 - Invariant measures for interval translations and some other piecewise continuous maps

AU - Kryzhevich, Sergey

N1 - Publisher Copyright: © EDP Sciences, 2020.

PY - 2020/3/12

Y1 - 2020/3/12

N2 - We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.

AB - We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.

KW - Krylov-Bogolybov theorem

KW - invariant measures

KW - periodic points

KW - piecewise continuous maps

KW - piecewise isometries

KW - interval translation maps

KW - Periodic points

KW - Interval translation maps

KW - Invariant measures

KW - Piecewise isometries

KW - Piecewise continuous maps

UR - http://www.scopus.com/inward/record.url?scp=85088161615&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/fb329693-4396-362f-8204-02cb18c59763/

U2 - 10.1051/mmnp/2019041

DO - 10.1051/mmnp/2019041

M3 - Article

VL - 15

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

M1 - 15

ER -

ID: 52303768