A nonautonomous C^r-topological equivalence involving contractions and unbounded nonlinearities

2023/10/15 by Castañeda, Álvaro, Torres, Fernanda
#37B25 #37C60 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.09936

Abstract

We study the smoothness of the topological equivalence between a linear equation and its nonlinear perturbation, which is regarded as unbounded. To the best of our knowledge, it has not previously been considered such study in the literature. Therefore, the main result of this work copes with this lack, that is, it is shown, on the positive half line, that such topological equivalence is of class C^r (r ≥ 1) when the linear part is a uniform contraction and the nonlinearities considered are unbounded.

Related

• Smoothness of Topological Equivalence on the Half Line for Nonautonomous\n Systems
• Topological Equivalence of nonautonomous difference equations with a\n family of dichotomies on the half line
• Sharpness of C⁰ conjugacy for the non-autonomous differential equations with Lipschitzian perturbation
• Linearization of a nonautonomous unbounded system with nonuniform contraction: A Spectral Approach
• A note on the differentiability of Palmer's topological equivalence for discrete systems