Bonckaert, PatrickNaudot, Vincent2022-08-172022-08-172017-10-24Bonchaert, P., & Naudot, V. (2017). Linearization of hyperbolic resonant fixed points of diffeomorphisms with related Gevrey estimates in the planar case. Electronic Journal of Differential Equations, 2017(266), pp. 1-29.1072-6691https://hdl.handle.net/10877/16067We 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.Text29 pages1 file (.pdf)enAttribution 4.0 InternationalPoincare Dulac normal formConjugacyNormal formMourtada type functionTag monomial Gevrey asymptoticArticle