Linearization of families of germs of hyperbolic vector fields

Abstract

In this article, we develop some techniques to linearize families of smooth vector fields in a neighbourhood of a hyperbolic equilibrium point. In particular, we present the linearizing conjugacy in an explicit way and describe the smoothness of the conjugacy in terms of the eigenvalues of the vector fields.

Keywords:

• differential equations
• normalization
• linearization
• resonance

2000 Mathematics Subject Classifications:

• Primary 34K17
• 37C15

Acknowledgements

We are very grateful to the referees for their helpful remarks and suggestions.