Comparison of averages of flows and maps

Details Comparison of averages of flows and maps Comparison of averages of flows and maps

2001-05-22

arxiv.org/abs/nlin/0105050v1

Nonlinear Sciences

Chaotic Dynamics

4 pages in Revtex with 2 included postscript figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.64.055206

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to permanent chaos, results obtained from the Poincare map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincare surface becomes relevant. However, after introducing a true-time Poincare map, quantities known from the usual Poincare map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g. Liapunov exponents and drifts can be determined correctly using these novel measures. Significant differences become evident when we compare with results obtained from the usual Poincare map.

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