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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Persistent chaos in high dimensions
J. Crutchfield, David Albers and J. SprottAbstract
n extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.
- Received:
- 27.10.05
- Published:
- 27.10.05
- MSC Codes:
- 37-XX, 34-XX
- PACS:
- 05., 87.18.Sn, 95.10.Fh
- Keywords:
- higd-dimensional dynamics, stability conjecture, highientropy