1. Regularity of Center Manifolds via the Graph Transform.
- Author
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Sandstede, Björn and Theerakarn, Thunwa
- Subjects
- *
LIPSCHITZ spaces , *CENTER manifolds (Mathematics) , *DIFFERENTIABLE functions , *EIGENVALUES , *GRAPH theory - Abstract
The purpose of this paper is to give a short self-contained proof of the center-manifold theorem for maps and vector fields in finite-dimensional spaces using the graph transform. In particular, regularity of the center manifold is established using a direct argument that is based on the closedness of sets of differentiable functions whose highest derivatives are Lipschitz continuous in the space of continuous functions; this argument avoids the fiber contraction theorem that is commonly used in this context. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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