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 $L^1(X,m)$ generated by the dynamical system. This result is called the Variational principle and is similar to the classical variational principle for the topological pressure.