Preprint
An Invariant Manifold Theory for ODEs and Its Applications
arXiv (Cornell University)
06 Sep 2009
Abstract
For a system of ODEs defined on an open, convex domainUcontaining a positively invariant setΓ , we prove that under appropriate hypotheses,Γis the graph of aCʳfunction and thus aCʳmanifold. Because the hypotheses can be easily verified by inspecting the vector field of the system, this invariant manifold theory can be used to study the existence of invariant manifolds in systems involving a wide range of parameters and the persistence of invariant manifolds whose normal hyperbolicity vanishes when a small parameter goes to zero. We apply this invariant manifold theory to study three examples and in each case obtain results that are not attainable by classical normally hyperbolic invariant manifold theory.
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Details
- Title
- An Invariant Manifold Theory for ODEs and Its Applications
- Creators
- Dennis Guang Yang
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022203338804721