Mathematics – Dynamical Systems
Scientific paper
2008-09-18
Ergod. Th. & Dynam. Sys. (2011) V. 31. P. 995--1042
Mathematics
Dynamical Systems
51 pages, v.2: editorial corrections
Scientific paper
10.1017/S0143385710000210
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 it is a topological Markov chain. As the main summands these principles contain the integrals over invariant measures and the Kolmogorov--Sinai entropy. In the article 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.
Antonevich A. B.
Bakhtin V. I.
Lebedev Alexander V.
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