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}
}