H. Lustfeld

It is shown that in repelling systems (i.e. in transient chaos) no direct relations exist between averages in a continuous time dynamical system (flow) and averages over the corresponding Poincare map. However, this relation is restored if a time dependent Poincare map is defined instead of the usual one. The properties of such maps with regard to escape rates, measures, shifts, and Lyapunov exponents are investigated in general and in particular for one dimensional systems.