The infimum of Lipschitz constants in the conjugacy class of an interval map

@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 a 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, roč.~147, č.~1, s.~255-269. ISSN~0002-9939. Dostupné z: https://dx.doi.org/10.1090/proc/14255.