We give geometric proofs for the Grobman-Hartman theorem for diffeomorphisms and ODEs. Proofs use covering relations and cone conditions for maps and isolating segments and cone conditions for ODEs. We establish topological versions of the Grobman-Hartman theorem as the existence of some semiconjugaces.
"Topological shadowing and the Grobman-Hartman theorem." Topol. Methods Nonlinear Anal. 50 (2) 757 - 785, 2017. https://doi.org/10.12775/TMNA.2017.044