From Attractor to Chaotic Saddle: a journey through transverse instability
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Although not a generic situation in the broadest sense, many smooth dynamical systems defined by flows or maps leave certain submanifolds of the phase space invariant. This situation can become generic if appropriate constraints are imposed – for instance, if the system has a symmetry. However, there are many other situations in which this is the case, such as in evolutionary dynamics, synchronization of chaotic oscillators and systems with hidden symmetries.
KeywordsInvariant Measure Periodic Point Unstable Manifold Chaotic Attractor Normal Spectrum
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