Free energy and equilibrium states for families of interval maps
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We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit measure will have free energy at least that of the limit of the free energies. From this, we deduce results concerning existence and continuity of equilibrium states (statistical stability). Counterexamples to statistical stability in the absence of strong hypotheses are provided.
Dobbs , N & Todd , M J 2020 , ' Free energy and equilibrium states for families of interval maps ' , Memoirs of the American Mathematical Society , vol. 0 , pp. 7-108 .
Memoirs of the American Mathematical Society
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DescriptionFunding: MT was partially supported by FCT grant SFRH/BPD/26521/2006 and NSF grants DMS0606343 and DMS 0908093. ND was supported by ERC Bridges project, the Academy of Finland CoE in Analysis and Dynamics Research and an IBM Goldstine fellowship.
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