2017/05/31 by Julien Sedro
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differentiable function #Fixed point #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Order (exchange) #Pure mathematics #Series (stratigraphy) #Taylor series #math.DS
paper · pdf · doi:10.1088/1361-6544/aaa10b
25 pages; Accepted for publication in Nonlinearity; Revised version after referees reports
arxiv created 2017/12/01 · openalex publication_date 2018/03/05 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition operators acting on spaces of functions with finite regularity. We generalize this approach to higher order differentiability, through the notion of an n-graded family . We then give applications to the fixed point of a nonlinear map, and to linear response in the context of (uniformly) expanding dynamics (theorem 3 and corollary 2), in the spirit of Gouëzel–Liverani.