On t-entropy and variational principle for the spectral radii of transfer and weighted shift operators

The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations and the principal results have been achieved in the situation...

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Published inErgodic theory and dynamical systems Vol. 31; no. 4; pp. 995 - 1042
Main Authors ANTONEVICH, A. B., BAKHTIN, V. I., LEBEDEV, A. V.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2011
Subjects
Dynamical systems
Entropy
Integrals
Invariants
Mathematical analysis
Mathematics
Operators
Spectra
Variational principles
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Summary:The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations and the principal results have been achieved in the situation when the dynamical system is either reversible or a topological Markov chain. As the main summands, these principles contain the integrals over invariant measures and the Kolmogorov–Sinai entropy. In the paper we derive the variational principle for an arbitrary dynamical system. It gives the explicit description of the Legendre dual object to the spectral potential. It is shown that in general this principle contains not the Kolmogorov–Sinai entropy but a new invariant of entropy type—the t-entropy.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385710000210