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arXiv · 0809.3106

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

V. I. Bakhtin
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Abstract

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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V. I. Bakhtin. 2008-12-28. T-entropy and Variational principle for the spectral radius of weighted shift operators. https://doi.org/10.1017/s0143385709000716

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