on Dynamical Systems and Related Topics c©2008 ICMS in KAIST ENTROPY AND MEASURE DEGENERACY FOR FLOWS

Abstract. In discrete dynamical systems topological entropy is a topological invariant and a measurement of the complexity of a system. In continuous dynamical systems, in general, topological entropy defined as usual by the time one map does not work so well in what concerns these aspects. The point is that the natural notion of equivalence in the discrete case is topological conjugacy which preserves time while in the continuous case the natural notion of equivalence is topological equivalence which allow reparametrizations of the orbits. The main issue happens in the case that the system has fixed points and will be our subject here. 1