Characterizing isochronous points and computing isochronous sections

DOI10.1016/j.jmaa.2009.02.007zbMath1208.34034OpenAlexW2019913171MaRDI QIDQ1022958

Antonio Algaba, Manuel Reyes

Publication date: 10 June 2009

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.2009.02.007

zbMATH Keywords

centrescommutatorsfociisochronous sectionsnormalized vector fields

Mathematics Subject Classification ID

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

Related Items (11)

Phase portraits of uniform isochronous centers with homogeneous nonlinearities ⋮ Isochronous properties in fractal analysis of some planar vector fields ⋮ Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities ⋮ The isochronous center for Kukles homogeneous systems of degree eight ⋮ Isochronicity and normal forms of polynomial systems of ODEs ⋮ The isochronous centers for Kukles homogeneous system of degree nine ⋮ Simultaneous bifurcation of limit cycles and critical periods ⋮ Divergence and Poincaré-Liapunov constants for analytic differential systems ⋮ Limit Cycles on Piecewise Smooth Vector Fields with Coupled Rigid Centers ⋮ Phase portraits of uniform isochronous quartic centers ⋮ Isochronous and strongly isochronous foci of polynomial Liénard systems

Cites Work

• On period functions of Liénard systems
• Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies
• Characterizing isochronous centres by Lie brackets
• Centers with degenerate infinity and their commutators.
• Non-periodic isochronous oscillations in plane differential systems
• Normal forms for certain singularities of vectorfields
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Bifurcation of Critical Periods for Plane Vector Fields
• Isochronous centres and foci via commutators and normal forms
• Characterization of isochronous foci for planar analytic differential systems
• Isochronicity via normal form
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