ROTH, Samuel Joshua and Josef BOBOK. The infimum of Lipschitz constants in the conjugacy class of an interval map. Proceedings of the American Mathematical Society. Providence: American Mathematical Society, 2019, vol. 147, No 1, p. 255-269. ISSN 0002-9939. Available from: https://dx.doi.org/10.1090/proc/14255. |
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@article{30278, author = {Roth, Samuel Joshua and Bobok, Josef}, article_location = {Providence}, article_number = {1}, doi = {http://dx.doi.org/10.1090/proc/14255}, keywords = {Interval map; Lipschitz constant; topological entropy; countable Markov shift}, language = {eng}, issn = {0002-9939}, journal = {Proceedings of the American Mathematical Society}, title = {The infimum of Lipschitz constants in the conjugacy class of an interval map}, url = {http://www.ams.org/journals/proc/2019-147-01/S0002-9939-2018-14255-0/}, volume = {147}, year = {2019} }
TY - JOUR ID - 30278 AU - Roth, Samuel Joshua - Bobok, Josef PY - 2019 TI - The infimum of Lipschitz constants in the conjugacy class of an interval map JF - Proceedings of the American Mathematical Society VL - 147 IS - 1 SP - 255-269 EP - 255-269 PB - American Mathematical Society SN - 00029939 KW - Interval map KW - Lipschitz constant KW - topological entropy KW - countable Markov shift UR - http://www.ams.org/journals/proc/2019-147-01/S0002-9939-2018-14255-0/ L2 - http://www.ams.org/journals/proc/2019-147-01/S0002-9939-2018-14255-0/ N2 - How can we interpret the infimum of Lipschitz constants in the conjugacy class of an interval map? For a positive entropy map f, the exponential exp h(f) of the topological entropy gives a well-known lower bound. In the case of a countably piecewise monotone map that is topologically mixing and Markov, we characterize the infimum.(f) of Lipschitz constants as the exponential of the Salama entropy of a certain reverse Markov chain associated with the map. Dynamically, this number represents the exponential growth rate of the number of iterated preimages of nearly any point; we show that it can be strictly larger than exp h(f). In addition we prove that if f is piecewise monotone or C-infinity, these two quantities.(f) and exph(f) are equal. ER -
ROTH, Samuel Joshua and Josef BOBOK. The infimum of Lipschitz constants in the conjugacy class of an interval map. \textit{Proceedings of the American Mathematical Society}. Providence: American Mathematical Society, 2019, vol.~147, No~1, p.~255-269. ISSN~0002-9939. Available from: https://dx.doi.org/10.1090/proc/14255.
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