Entropy of a symbolic extension of a dynamical system

Residual entropy of a topological system is defined as the infimum increase of entropy necessary to build a symbolic extension of this system. If no s ymbolic extension exists then residual entropy is set at infinity. In this paper we provide a direct formula for the residual entropy of a system on a totally disconnected compact space in terms of basic notions of conditiona l entropies viewed as functions of invariant measures. This formula allows us to evaluate residual entropy in many examples as well as to construct ne w examples with arbitrarily preset topological and residual entropies. The appendix contains a condition equivalent to asymptotic h-expansiveness.