Differentiability with respect to parameters in global smooth linearization

Author(s)

Rodrigues, Hildebrando M. ^[1] ; Sola-Morales, J.

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP, Brazil. Sola-Morales, J., Univ Politecn Cataluna, ETSEIB, Dept Matemat, Ave Diagonal 647, E-08028 Barcelona - Spain

• Document type: Journal article
• Source: Journal of Differential Equations; v. 262, n. 6, p. 3583-3596, MAR 15 2017.
• Web of Science Citations: 1

Abstract

Let X be a Banach space and T-theta : X -> X a family of invertible contractions, T-theta = L-theta + f(theta), where L-theta is linear and f(theta) is nonlinear with f(theta)(0) = 0. We give conditions for the existence of a family of global linearization maps H-theta, such that H-theta o T-theta o H-theta(-1) = L-theta, with a smooth dependence on (theta). The results depend strongly on the choice of some appropriate spaces of maps, adapted norms and the use of a specific fixed point theorem with smooth dependence on parameters. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 15/19883-5 - Nonlinear Dynamical Systems and Applications.
• Grantee: Hildebrando Munhoz Rodrigues
• Support Opportunities: Regular Research Grants