Analytic Classification of Germs of Parabolic Antoholomorphic Diffeomorphisms of Codimension k
Dynamical Systems
2020-01-20 v1 Complex Variables
Abstract
We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic fixed point under analytic conjugacy. We then study some geometric applications: existence of real analytic invariant curve, existence of holomorphic and antiholomorphic roots of holomorphic and antiholomorphic parabolic germs, commuting holomorphic and antiholomorphic parabolic germs.
Keywords
Cite
@article{arxiv.2001.06428,
title = {Analytic Classification of Germs of Parabolic Antoholomorphic Diffeomorphisms of Codimension k},
author = {Jonathan Godin and Christiane Rousseau},
journal= {arXiv preprint arXiv:2001.06428},
year = {2020}
}
Comments
42 pages, 19 figures