Journal of Dynamics and Differential Equations

, Volume 27, Issue 3–4, pp 989–1006 | Cite as

Regularity of Center Manifolds via the Graph Transform

  • Björn SandstedeEmail author
  • Thunwa Theerakarn


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.


Center manifolds Graph transform Regularity 

Mathematics Subject Classification

37G10 34C23 37L10 



Sandstede was partially supported by the NSF through Grant DMS-0907904. Theerakarn acknowledges support by Brown University through an Undergraduate Teaching and Research Award. This paper is dedicated to the memory of Professor Klaus Kirchgässner: he was a terrific mentor and an engaged researcher who continues to be an inspiration to many of us.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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