The infimum of Lipschitz constants in the conjugacy class of an interval map
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F19%3AA0000052" target="_blank" >RIV/47813059:19610/19:A0000052 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21110/19:00325604
Result on the web
<a href="http://www.ams.org/journals/proc/2019-147-01/S0002-9939-2018-14255-0/" target="_blank" >http://www.ams.org/journals/proc/2019-147-01/S0002-9939-2018-14255-0/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/14255" target="_blank" >10.1090/proc/14255</a>
Alternative languages
Result language
angličtina
Original language name
The infimum of Lipschitz constants in the conjugacy class of an interval map
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
1088-6826
Volume of the periodical
147
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
255-269
UT code for WoS article
000450363900022
EID of the result in the Scopus database
2-s2.0-85061617973