Normal Hyperbolicity and Unbounded Critical Manifolds

Details Normal Hyperbolicity and Unbounded Critical Manifolds Normal Hyperbolicity and Unbounded Critical Manifolds

2012-04-04

arxiv.org/abs/1204.0947v1

Mathematics

Dynamical Systems

preprint version 1; comments and suggestions very welcome

Scientific paper

This paper is motivated by open mathematical questions arising in differential equation models for autocatalytic reactions. We extend the local theory of singularities in fast-slow polynomial vector fields to classes of unbounded critical manifolds related to a loss of normal hyperbolicity for associated slow manifolds. A projective transformation is used to localize the unbounded problem and the blow-up method is employed to characterize the breakdown regime for slow manifolds. Our analysis yields a scaling law for all unbounded manifolds which exhibit a power-law decay for the alignment with a fast subsystem domain.

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