We consider a symbolic dynamical system (x, alpha) on a countable state space. We introduce a kind of topological entropy for such systems, denoted h, which coincides with usual topological entropy when x is compact. We use a pictorial approach, to classify a graph (or a chain) as transient, null recurrent, or positive recurrent. We show that given 0 < or = alpha < = beta < or infinity, there is a chain whose h entropy is beta and where Gurevic entropy is alpha. We compute the topological entropies of some classes of chains, including larger chains built up from smaller ones by a new operation which we call the Cartesian sum. Keywords: Reprints.
展开▼
