THE HARTMAN-GROBMAN THEOREM FOR REVERSIBLE-SYSTEMS ON BANACH-SPACES

In this note we give a version of the Hartman-Grobman Theorem for reve rsible systems defined on a Banach space. We prove that the homeomorph ism that reduces the nonlinear system to the linearized one preserves the symmetry. Applications to coupled nonlinear second-order ordinary differential equations and to coupled nonlinear wave equations are dis cussed.