Preprint
Breakdown of Normal Hyperbolicity for a Family of Invariant Manifolds with Generalized Lyapunov-Type Numbers Uniformly Bounded below Their Critical Values
arXiv (Cornell University)
30 Dec 2009
Abstract
We present three examples to illustrate that in the continuation of a family of normally hyperbolicC¹manifolds, the normal hyperbolicity may break down as the continuation parameter approaches a critical value even though the corresponding generalized Lyapunov-type numbers remain uniformly bounded below their critical values throughout the process. In the first example, aC¹manifold still exists at the critical parameter value, but it is no longer normally hyperbolic. In the other two examples, at the critical parameter value the family ofC¹manifolds converges to a nonsmooth invariant set, for which generalized Lyapunov-type numbers are undefined.
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Details
- Title
- Breakdown of Normal Hyperbolicity for a Family of Invariant Manifolds with Generalized Lyapunov-Type Numbers Uniformly Bounded below Their Critical Values
- Creators
- Dennis Guang Yang
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022203172704721