The Markus-Yamabe conjecture does not hold for discontinuous piecewise linear differential systems separated by one straight line

DOI10.1007/s10884-020-09825-8zbMath1480.34074OpenAlexW3003688214WikidataQ122961876 ScholiaQ122961876MaRDI QIDQ2025669

Jaume Llibre, Lucyjane de A. S. Menezes

Publication date: 14 May 2021

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-020-09825-8

zbMATH Keywords

Markus-Yamabe conjecturediscontinuous piecewise linear differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Global stability of solutions to ordinary differential equations (34D23)

Related Items (2)

The Markus-Yamabe conjecture for discontinuous piecewise linear differential systems in \(\mathbb{R}^n\) separated by a \(\mathrm{conic} \!\times \! \mathbb{R}^{n-2}\) ⋮ Dynamics analysis of Llibre-Menezes piecewise linear systems

Cites Work

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• A polynomial class of Markus–Yamabe counterexamples and examples in ℝ³
• Global stability of equilibria
• Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels
• A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization

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