Arcwise connectedness of the set of ergodic measures of hereditary shifts

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00493628" target="_blank" >RIV/67985556:_____/18:00493628 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/proc/14029" target="_blank" >http://dx.doi.org/10.1090/proc/14029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/14029" target="_blank" >10.1090/proc/14029</a>

Result language
angličtina
Original language name
Arcwise connectedness of the set of ergodic measures of hereditary shifts
Original language description
We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $ d$-bar metric. As a consequence the set of ergodic measures of such a shift is also arcwise connected in the weak-star topology, and the entropy function over this set attains all values in the interval between zero and the topological entropy of the shift (inclusive). The latter result is motivated by a conjecture of A. Katok.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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