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arXiv · 1604.05241

The Poincar\'e-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations

J. B. van den Berg·S. Munao·R. C. A. M. Vandervorst
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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.

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J. B. van den Berg, S. Munao, R. C. A. M. Vandervorst. 2016-04-18. The Poincar\'e-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations. https://doi.org/10.1016/j.physd.2016.04.009

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