On $p$-adic entropy of some solenoid dynamical systems

To a dynamical system is attached non-negative real number called entropy. In 1990, Lind, Schmidt and Ward proved that the entropy for induced by Laurent polynomial algebra over ring of rational integers described Mahler measure. 2009, Deninger introduced $p$-adic obtained analogue Lind-Schmidt-Ward's theorem using measures. this paper, we prove existence explicit formula about entropies two systems; one field $K$, other defined solenoid.