From attractor to chaotic saddle: A tale of transverse instability
UNSPECIFIED (1996) From attractor to chaotic saddle: A tale of transverse instability. NONLINEARITY, 9 (3). pp. 703-737. ISSN 0951-7715Full text not available from this repository.
Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for the original system, and in what sense? We characterize the transverse dynamics near A in terms of the normal Liapunov spectrum of A. In particular, we emphasize the role of invariant measures on A. Our results identify the points at which A: (1) ceases to be asymptotically stable, possibly developing a locally riddled basin; (2) ceases to be an attractor; (3) becomes a transversely repelling chaotic saddle. We show, in the context of what we call 'normal parameters' how these transitions can be viewed as being robust. Finally, we discuss some numerical examples displaying these transitions.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Journal or Publication Title:||NONLINEARITY|
|Publisher:||IOP PUBLISHING LTD|
|Number of Pages:||35|
|Page Range:||pp. 703-737|
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