Linearization of hyperbolic resonant fixed points of diffeomorphisms with related Gevrey estimates in the planar case
Date
2017-10-24
Authors
Bonckaert, Patrick
Naudot, Vincent
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We show that any germ of smooth hyperbolic diffeomophism at a fixed point is conjugate to its linear part, using a transformation with a Mourtada type functions, which (roughly) means that it may contain terms like x log |x|. Such a conjugacy admits a Mourtada type expansion. In the planar case, when the fixed point is a p:-q resonant saddle, and if we assume that the diffeomorphism is of Gevrey class, we give an upper bound on the Gevrey estimates for this expansion.
Description
Keywords
Poincare Dulac normal form, Conjugacy, Normal form, Mourtada type function, Tag monomial Gevrey asymptotic
Citation
Bonchaert, P., & Naudot, V. (2017). Linearization of hyperbolic resonant fixed points of diffeomorphisms with related Gevrey estimates in the planar case. <i>Electronic Journal of Differential Equations, 2017</i>(266), pp. 1-29.
Rights
Attribution 4.0 International