The Poincar\'e-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations
Analysis of PDEs
2016-10-12 v1 Differential Geometry
Dynamical Systems
Abstract
Fiedler and Mallet-Paret prove a version of the classical Poincar\'e-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy-Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapunov function.
Keywords
Cite
@article{arxiv.1604.05241,
title = {The Poincar\'e-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations},
author = {J. B. van den Berg and S. Munao and R. C. A. M. Vandervorst},
journal= {arXiv preprint arXiv:1604.05241},
year = {2016}
}
Comments
5 figures