2022
DOI: 10.48550/arxiv.2201.12945
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Higher regularity of homeomorphisms in the Hartman-Grobman theorem and a conjecture on its sharpness

Abstract: Hartman-Grobman theorem states that there is a homeomorphism H sending the solutions of the nonlinear system onto those of its linearization under suitable assumptions.Many mathematicians have made contributions to prove Hölder continuity of the homeomorphisms. However, is it possible to improve the Hölder continuity to Lipschitzian continuity? This paper gives a positive answer. We formulate the first result that the homeomorphism is Lipschitzian, but not C 1 , while its inverse is merely Hölder continuous, b… Show more

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