Abstract
For systems of ordinary differential equations admitting linear automorphisms, we consider the problems of smooth equivalence and linearization preserving these automorphisms.
Similar content being viewed by others
References
A. Afendikov and A. Mielke,Bifurcation of Homoclinic Orbits to a Saddle-Focus in Reversible Systems With SO(2)-symmetry, Preprint DANCE No., 1, Universität Hannover, Hannover, Germany (1998).
A. D. Bryuno,A Local Method of Nonlinear Analysis for Differential Equations [in Russian], Nauka, Moscow (1979).
Ph. Hartman,Ordinary Differential Equations, Wiley, New York-London-Sydney (1964).
V. S. Samovol, “Equivalence of systems of differential equations in the neighborhood of a singular point,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],44, 213–234 (1982).
V. S. Samovol, “A necessary and sufficient condition for a smooth linearization of an autonomous system on the plane in a neighborhood of a singular point,”Mat. Zametki [Math. Notes],46, No. 1, 67–77 (1989).
V. S. Samovol, “Linearization of systems of differential equations in the neighborhood of invariant toroidal manifolds,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],38, 187–219 (1979).
V. S. Samovol, “A criterion forC 1-smooth linearization of an autonomous system in a neighborhood of a nondegenerate singular point,”Mat. Zametki [Math. Notes],49, No. 3, 91–96 (1991).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 567–578, October, 1999.
Rights and permissions
About this article
Cite this article
Samovol, V.S. Smooth equivalence of differential equations and linear automorphisms. Math Notes 66, 464–473 (1999). https://doi.org/10.1007/BF02679097
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02679097