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@article{49220, author = {Bartoš, Adam and Bobok, Jozef and Pyrih, Pavel and Roth, Samuel Joshua and Vejnar, Benjamin}, article_location = {New York}, article_number = {11}, doi = {http://dx.doi.org/10.1017/etds.2019.29}, keywords = {Markov map; tame graph; constant slope; conjugacy; entropy}, language = {eng}, issn = {0143-3857}, journal = {Ergodic Theory and Dynamical Systems}, title = {Constant slope, entropy, and horseshoes for a map on a tame graph}, url = {https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/constant-slope-entropy-and-horseshoes-for-a-map-on-a-tame-graph/92747064767B5DC745355B2ED02C6071}, volume = {40}, year = {2020} }
TY - JOUR ID - 49220 AU - Bartoš, Adam - Bobok, Jozef - Pyrih, Pavel - Roth, Samuel Joshua - Vejnar, Benjamin PY - 2020 TI - Constant slope, entropy, and horseshoes for a map on a tame graph JF - Ergodic Theory and Dynamical Systems VL - 40 IS - 11 SP - 2970-2994 EP - 2970-2994 PB - Cambridge University Press SN - 01433857 KW - Markov map KW - tame graph KW - constant slope KW - conjugacy KW - entropy UR - https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/constant-slope-entropy-and-horseshoes-for-a-map-on-a-tame-graph/92747064767B5DC745355B2ED02C6071 N2 - 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. ER -
BARTOŠ, Adam, Jozef BOBOK, Pavel PYRIH, Samuel Joshua ROTH a Benjamin VEJNAR. Constant slope, entropy, and horseshoes for a map on a tame graph. \textit{Ergodic Theory and Dynamical Systems}. New York: Cambridge University Press, 2020, roč.~40, č.~11, s.~2970-2994. ISSN~0143-3857. Dostupné z: https://dx.doi.org/10.1017/etds.2019.29.
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