The poincaré manifold at a stable equilibrium of c² planar flow

Abstract

We establish the existence of a unique C² local invariant manifold at the stable equilibrium of a C² vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/⋋ is bounded above by the degree of smoothness of the vector field.

Keywords:

• Weak stable mainfield
• Generalized center stanle mainflod
• Poincaré Mainfold
• strong stable mainfold
• Nonresonance ineauailty
• Local invant manifold