Limit cycles bifurcating from isochronous surfaces of revolution in \(\mathbb R^3\)

DOI10.1016/j.jmaa.2011.04.009zbMath1225.34039OpenAlexW1976271680MaRDI QIDQ541267

Jaume Llibre, Joan Torregrosa, Salomón Rebollo-Perdomo

Publication date: 6 June 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.04.009

zbMATH Keywords

periodic orbitaveraging methodisochronous setLimit cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (6)

Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder ⋮ Bifurcation of limit cycles for a family of perturbed Kukles differential systems ⋮ On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations ⋮ Bifurcation of piecewise smooth manifolds from 3D center-type vector fields ⋮ Improving the averaging theory for computing periodic solutions of the differential equations ⋮ Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

Cites Work

• Limit cycles of differential equations
• Limit cycles bifurcating from a two-dimensional isochronous cylinder
• Tchebycheff systems and best partial bases
• Periodic solutions of nonlinear periodic differential systems with a small parameter
• Limit cycles bifurcating from a \(k\)-dimensional isochronous center contained in \(\mathbb R^n\) with \(k\leqslant n\)
• Limit Cycles Bifurcating from a 2-Dimensional Isochronous Torus in ℝ³
• Averaging methods in nonlinear dynamical systems
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