Certain differential equations have only isolated periodic orbits

DOI10.1007/BF01789396zbMath0561.34028OpenAlexW2076319503MaRDI QIDQ2266367

Russell A. Smith

Publication date: 1984

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01789396

zbMATH Keywords

isolated periodic orbitsautonomous analytic differential equationsPoincaré's isolation theorem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

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Method of ``transition into space of derivatives: 40 years of evolution ⋮ Massera's convergence theorem for periodic nonlinear differential equations ⋮ Orbital stability for ordinary differential equations ⋮ Unnamed Item ⋮ Some modified Michaelis–Menten equations having stable closed trajectories ⋮ The torus principle for three-dimensional analytic autonomous systems having negative divergence ⋮ Abstract competitive systems and orbital stability in $\mathbf{{\mathbb R}^3}$ ⋮ Unnamed Item

Cites Work

• Some theorems on the inertia of general matrices
• Snakes: oriented families of periodic orbits, their sources, sinks, and continuation
• Matrices \(C\) with \(C^ n\to 0\)
• Existence of periodic orbits of autonomous ordinary differential equations
• An index theorem and Bendixson's negative criterion for certain differential equations of higher dimension
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