T-entropy and Variational principle for the spectral radius of weighted shift operators

Details T-entropy and Variational principle for the spectral radius of weighted shift operators T-entropy and Variational principle for the spectral radius of weighted shift operators

2008-09-18

arxiv.org/abs/0809.3106v2

Ergod. Th. & Dynam. Sys. (2010) V. 30. P. 1331--1342

Mathematics

Dynamical Systems

12 pages, v.2: editorial corrections

Scientific paper

10.1017/S0143385709000716

In this paper we introduce a new functional invariant of discrete time dynamical systems -- the so-called t-entropy. The main result is that this t-entropy is the Legendre dual functional to the logarithm of the spectral radius of the weighted shift operator on $L^1(X,m)$ generated by the dynamical system. This result is called the Variational principle and is similar to the classical variational principle for the topological pressure.

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