Podrobný výpis o publikaci

BARTOŠ, Adam, Jozef BOBOK, Pavel PYRIH, Samuel Joshua ROTH a Benjamin VEJNAR. Constant slope, entropy, and horseshoes for a map on a tame graph. Ergodic Theory and Dynamical Systems. New York: Cambridge University Press, roč. 40, č. 11, s. 2970-2994. ISSN 0143-3857. doi:10.1017/etds.2019.29. 2020.

Další formáty: BibTeX LaTeX RIS

Základní údaje
Originální název	Constant slope, entropy, and horseshoes for a map on a tame graph
Autoři	BARTOŠ, Adam (203 Česká republika), Jozef BOBOK (203 Česká republika), Pavel PYRIH (203 Česká republika), Samuel Joshua ROTH (840 Spojené státy, domácí) a Benjamin VEJNAR (203 Česká republika).
Vydání	Ergodic Theory and Dynamical Systems, New York, Cambridge University Press, 2020, 0143-3857.

Další údaje
Originální jazyk	angličtina
Typ výsledku	Článek v odborném periodiku
Obor	10101 Pure mathematics
Stát vydavatele	Spojené státy
Utajení	není předmětem státního či obchodního tajemství
WWW	Ergodic Theory and Dynamical Systems
Kód RIV	RIV/47813059:19610/20:A0000076
Organizační jednotka	Matematický ústav v Opavě
Doi	http://dx.doi.org/10.1017/etds.2019.29
UT WoS	000573869900004
Klíčová slova anglicky	Markov map; tame graph; constant slope; conjugacy; entropy
Štítky	MÚ
Příznaky	Mezinárodní význam, Recenzováno
Změnil	Změnil: Mgr. Aleš Ryšavý, učo 28000. Změněno: 17. 3. 2021 12:38.

Anotace
We study continuous countably (strictly) monotone maps defined on a tame graph, i.e. a special Peano continuum for which the set containing branch points and end points has countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map f of a tame graph G is conjugate to a map g of constant slope. In particular, we show that in the case of a Markov map f that corresponds to a recurrent transition matrix, the condition is satisfied for a constant slope e(htop(f)), where e(htop(f))is the topological entropy of f. Moreover, we show that in our class the topological entropy e(htop(f)) is achievable through horseshoes of the map f.

Anotace

We study continuous countably (strictly) monotone maps defined on a tame graph, i.e. a special Peano continuum for which the set containing branch points and end points has countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map f of a tame graph G is conjugate to a map g of constant slope. In particular, we show that in the case of a Markov map f that corresponds to a recurrent transition matrix, the condition is satisfied for a constant slope e(htop(f)), where e(htop(f))is the topological entropy of f. Moreover, we show that in our class the topological entropy e(htop(f)) is achievable through horseshoes of the map f.