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

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 L1(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.