This title appears in the Scientific Report :
2001
Please use the identifier:
http://dx.doi.org/10.1103/PhysRevE.64.055206 in citations.
Please use the identifier: http://hdl.handle.net/2128/9252 in citations.
Comparison of averages of flows and maps
Comparison of averages of flows and maps
It is shown that in transient chaos there is no direct relation between averages in a continuous 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...
Saved in:
Personal Name(s): | Kaufmann, Z. |
---|---|
Lustfeld, H. | |
Contributing Institute: |
Theorie I; IFF-TH-I |
Published in: | Physical Review E Physical review / E, 64 64 (2001 2001) 5 5, S. 055206 055206 |
Imprint: |
College Park, Md.
APS
2001
2001-10-26 2001-10-01 |
Physical Description: |
1 |
DOI: |
10.1103/PhysRevE.64.055206 |
Document Type: |
Journal Article |
Research Program: |
Elektronische Struktur von Festkörpern, Oberflächen und Schichtsystemen |
Series Title: |
Physical Review E
64 |
Subject (ZB): | |
Link: |
OpenAccess OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/9252 in citations.
It is shown that in transient chaos there is no direct relation between averages in a continuous 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 measures. Significant differences become evident when we compare with results obtained from the usual Poincare map. |