On the C~1-Equivalence of Essentially Nonlinear Systems of Differential Equations Near an Asymptotically Stable Equilibrium Point

摘要

A system of differential equations is considered for which the origin is an asymptotically stable equilibrium point and the Taylor expansion in a neighborhood of this point has no linear terms. Under the assumption that the logarithmic norm of the Jacobian matrix is negative definite, it is proved that this system is locally C~1 equivalent to any of its perturbations of sufficiently high order of vanishing.