English

Fixed points of elliptic reversible transformations with integrals

Complex Variables 2009-09-25 v1

Abstract

We show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general reversible transformation with integrals. We also study the integrable holomorphic reversible transformations coming from real analytic surfaces in C^2 with non-degenerate complex tangents. We show the existence of real analytic surfaces with hyperbolic complex tangents, which are contained in a real hyperplane, but cannot be transformed into the Moser-Webster normal form through any holomorphic transformation.

Keywords

Cite

@article{arxiv.math/9506201,
  title  = {Fixed points of elliptic reversible transformations with integrals},
  author = {Xianghong Gong},
  journal= {arXiv preprint arXiv:math/9506201},
  year   = {2009}
}