A fundamental problem that arises in dynamical systems in the study of the local behavior of a diffeomorphism or flow is the linearizability of the system near a fixed point. This is the question of whether there exists a local change of variable converting the system to a linear one. Grobman [G1; G2]and Hartman [Ha2; Ha3] proved that there is always a linearizing change of variable that is a homeomor- phism is the fixed point is hyperbolic. A fixed point of a diffeomorphism (resp. Flow) is hyperbolic if the derivative at the point has no eigenvalues on the unit cir- Cle (resp. Imaginary axis).
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