Hartman-Grobman theorem

Let U and V be open subsets of a Banach space E such that 0UV. If a diffeomorphismMathworldPlanetmath f:UV has 0 as a hyperbolic fixed pointMathworldPlanetmath, then f and Df(0) are locally topologically conjugateMathworldPlanetmath at 0, i.e. there are neighborhoodsMathworldPlanetmathPlanetmath U~ and V~ of 0 and a homeomorphismPlanetmathPlanetmath h:U~V~ such that Df(0)h=hf.

Title Hartman-Grobman theorem
Canonical name HartmanGrobmanTheorem
Date of creation 2013-03-22 14:25:15
Last modified on 2013-03-22 14:25:15
Owner Koro (127)
Last modified by Koro (127)
Numerical id 6
Author Koro (127)
Entry type Theorem
Classification msc 37C25
Synonym Grobman-Hartman theorem
Synonym Hartman’s theorem