On the explicit form of the Grobman-Hartman homeomorphisms for dissipative dynamical systems

Poincaré-Dulac normal forms together with time integration are used to obtain explicit forms of the Grobman-Hartman homeomorphism for a system of real ODEʹs with the linear part in the Poincaré domain. The homeomorphisms are at least C1 with powers of logarithms as singularities. We exemplarily apply the linearizing transformations to the equations of Fitzhugh-Nagumo and Lorenz, both 3D and 5D, in the subcritical regime. We also discuss interval normal forms which are continuous in some parameter interval.