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Publikační činnost

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Typ záznamu * :	článek v odborném periodiku (J)
Domácí pracoviště * :	Ústav pro výzkum a aplikace fuzzy modelování (94410)
Název * :	Periodic points and shadowing property for generic Lebesgue measure preserving interval maps
Citace :	Činč, J., Oprocha, P., Troubetzkoy, S. a Bobok, J. Periodic points and shadowing property for generic Lebesgue measure preserving interval maps. Nonlinearity. 2022, 35(April), s. 2534-2557.

Podnázev :
Rok * :	2022
Obor * :	Obecná matematika
Kód ISSN * :
Oficiální název periodika * :	Nonlinearity
Stát vydavatele periodika * :	Spojené království Velké Británie a Severního Irska
Svazek periodika * :	35
Číslo periodika v rámci svazku * :	April
Číslo článku :
Ročník :
Počet stran článku * :	25
Strana od * :	2534
Strana do * :	2557
Kód UT WoS :
EID :
Poddruh recenzovaného článku :	Článek v impaktovaném časopise (Jimp)

Klíčová slova anglicky * :	Interval map, circle map, Lebesgue measure preserving, periodic points, Hausdorff dimension, upper box dimension, shadowing, generic properties
Popis v původním jazyce * :	In this article we study dynamical behaviour of generic Lebesgue measure- preserving interval maps. We show that for each k greater or equal than 1 the set of periodic points of period at least k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Moreover, we obtain analogous results also in the context of generic Lebesgue measure-preserving circle maps. Furthermore, building on the former results, we show that there is a dense collection of transitive Lebesgue measure-preserving interval maps whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k greater of equal than 1. Finally, we show that the generic continuous maps of the inter- val which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.
Popis v anglickém jazyce * :	We show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k>0 that the set of periodic points of period k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Furthermore, building on this result, we show that there is a dense collection of transitive Lebesgue measure preserving interval map whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k>0. Finally, we show that the generic continuous maps of the interval which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.

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