Study of the period function of a two-parameter family of centers

DOI10.1016/j.jmaa.2017.02.054zbMath1372.34074OpenAlexW2591852366MaRDI QIDQ2400649

Yanyan Li

Publication date: 29 August 2017

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

Full work available at URL: http://ddd.uab.cat/record/182501

zbMATH Keywords

periodic orbitsbifurcation

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)

Related Items

The monotonicity of the apsidal angle using the theory of potential oscillators ⋮ Asymptotic development of an integral operator and boundedness of the criticality of potential centers ⋮ On the upper bound of the criticality of potential systems at the outer boundary using the Roussarie-Ecalle compensator ⋮ On the critical points of the flight return time function of perturbed closed orbits ⋮ Resonance of bounded isochronous oscillators ⋮ Analytic tools to bound the criticality at the outer boundary of the period annulus ⋮ A proof of Bertrand's theorem using the theory of isochronous potentials

Cites Work

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• Darboux linearization and isochronous centers with a rational first integral
• Rotated vector fields
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• The criticality of centers of potential systems at the outer boundary
• Criteria to bound the number of critical periods
• Keeping track of limit cycles
• The monotonicity of the period function for planar Hamiltonian vector fields
• Global bifurcation of steady-state solutions
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Isochronicity for several classes of Hamiltonian systems
• Algebraic and analytical tools for the study of the period function
• Monotonicity of the period function for \(u-u+u^p=0\) with \(p\in \mathbb R\) and \(p>1\)
• The period function of reversible quadratic centers
• A Chebyshev criterion for Abelian integrals
• Bifurcation of critical periods from Pleshkan's isochrones
• Cyclicity of period annuli and principalization of Bautin ideals
• A class of Hamiltonian systems with increasing periods.
• The number of limit cycles of certain polynomial differential equations
• Bifurcation of Critical Periods for Plane Vector Fields
• Local Bifurcations of Critical Periods in the Reduced Kukles System

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