Rescaled Poincar\'e map via blowup of singularities
Dynamical Systems
2017-09-22 v2
Abstract
Through blowup \cite{T}, the rescaled Poicar\'e map is continued to nondegenerate singularities in \cite{GY,CY}. For a nondegenerate singularity of a vector field, we prove that the extended rescaled Poincar\'e map over the singurity equals the counterpart of the vector field's linearization. For singularities of two dimensional linear vector fields of three types, we compute the rescaled Poincar\'e maps upto the second order. We show that except for the focus case, the second order generally does not vanish, and the rescaled Poincar\'e map is generally nonlinear.
Cite
@article{arxiv.1709.06241,
title = {Rescaled Poincar\'e map via blowup of singularities},
author = {Xiao Qianying},
journal= {arXiv preprint arXiv:1709.06241},
year = {2017}
}
Comments
Both the result and proof need to be checked and polished. And this work is not good enough to be called a research paper