Theory of Invariant Manifold and Foliation and Uniqueness of Center Manifold Dynamics.

Here we prove that the dynamics on any two center-manifolds of a fixed point of any C k , 1 dynamical system of finite dimension with k ≥ 1 are C k -conjugate to each other. For pedagogical purpose, we also extend Perron's method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions. [ABSTRACT FROM AUTHOR]