On the Hartman-Grobman theorem for maps
The Hartman-Grobman theorem says that in a neighborhood of a hyperbolic fixed point a diffeomorphism is topologically conjugate to its derivative at that fixed point. A generalization of this theorem to a hyperbolic automorphism L of a Banach space X is also known. The author extends this to the case of a hyperbolic endomorphism L of X. Namely, he proves that the maps \(\phi_ j=L+f_ j\), \(j=1,2\) where \(f_ j: X\to X\) are Lipschitz with \(lip(f_ j)\) small enough, are inverse limit conjugate by a homeomorphism which maps orbits of \(\phi_ 1\) to orbits of \(\phi_ 2\). An application to evolution equations is given.
scientific article; zbMATH DE number 3962806
scientific article