English

Generic unfolding of an antiholomorphic parabolic point of codimension $k$

Dynamical Systems 2023-01-30 v1

Abstract

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~kk (i.e.~a fixed point of multiplicity k+1k+1) under conjugacy. Such generic unfoldings depend real analytically on kk real parameters. A preparation of the unfolding allows to identify real analytic \emph{canonical parameters}, which are preserved by any conjugacy between two prepared generic unfoldings. A modulus of analytic classification is defined, which is an unfolding of the modulus assigned to the antiholomorphic parabolic point. Since the second iterate of such a germ is a real unfolding of a holomorphic parabolic point, the modulus is a special form of an unfolding of the \'Ecalle-Voronin modulus of the second iterate of the antiholomorphic parabolic germ. We also solve the problem of the existence of an antiholomorphic square root to a germ of generic analytic unfolding of a holomorphic parabolic germ.

Keywords

Cite

@article{arxiv.2301.11684,
  title  = {Generic unfolding of an antiholomorphic parabolic point of codimension $k$},
  author = {Christiane Rousseau},
  journal= {arXiv preprint arXiv:2301.11684},
  year   = {2023}
}

Comments

29 pages, 18 figures