Co-compact entropy and its variational principle for non-compact spaces

摘要

The purpose of this paper is to generalize the variational principle, whichstates that the topological entropy is equal to the supremum of the measuretheoretical entropies and also the minimum of the metric theoretical entropies,to non-compact dynamical systems by utilizing the co-compact entropy. Theequivalence between positive co-compact entropy and the existence ofp-horseshoes over the real line is also proved. This implies a system over realline with positive co-compact entropy contains a compact invariant subset.