2019/05/17 by Ignacio Huerta, Huerta, I. · 2 citations
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Numerical methods for differential equations #Control and Stability of Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1905.07319
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of homeomorphisms. The first one is set up by considering the fact that linear system is almost reducible to diagonal system with a small enough perturbation where the diagonal entries belong to spectrum of the nonuniform exponential dichotomy; and the second one is constructed in terms of the crossing times with respect to unit sphere of an adequate Lyapunov function associated to the linear system.