The parameterization method for invariant manifolds III: overview and applications

By Xavier Cabré Vilagut, Ernest Fontich i Julià, R. Canosa. 2003

231 citations recorded by the source corpus.

We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/128c2fb83f15e3a8482b36b0f76ec2b3a6120fe1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Xavier Cabré Vilagut
2. Ernest Fontich i Julià
3. R. Canosa
4. G. Haller

In Mathematical Physics

1. Xavier Cabré Vilagut
2. Ernest Fontich i Julià
3. R. Canosa
4. G. Haller

In Statistical and Nonlinear Physics

1. Xavier Cabré Vilagut
2. Ernest Fontich i Julià
3. R. Canosa
4. S. Ponsioen
5. G. Haller
6. Jerrold E. Marsden
7. Gary Froyland
8. Francois Lekien

Citations in the corpus

• Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction (2016, background): “[9] for a historical and technical survey), which forms the basis of some of the rigorous invariant manifold results we will use in the present paper.”
• The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces (2002, methodology): “, the expository work [CFdlL02]) it gives less differentiability for the solution.”