The Poincaré-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations

Abstract

Fiedler and Mallet-Paret prove a version of the classical Poincaré-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.

5 figures

Cited by in corpus (1)

• Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay