J
2020
Constant slope, entropy, and horseshoes for a map on a tame graph
BARTOŠ, Adam, Jozef BOBOK, Pavel PYRIH, Samuel Joshua ROTH, Benjamin VEJNAR et. al.
Basic information
Original name
Constant slope, entropy, and horseshoes for a map on a tame graph
Authors
BARTOŠ, Adam (203 Czech Republic), Jozef BOBOK (203 Czech Republic), Pavel PYRIH (203 Czech Republic), Samuel Joshua ROTH (840 United States of America, belonging to the institution) and Benjamin VEJNAR (203 Czech Republic)
Edition
Ergodic Theory and Dynamical Systems, New York, Cambridge University Press, 2020, 0143-3857
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/20:A0000076
Organization unit
Mathematical Institute in Opava
Keywords in English
Markov map; tame graph; constant slope; conjugacy; entropy
Tags
International impact, Reviewed
V originále
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.
Displayed: 24/12/2024 03:39