Analytic tools to bound the criticality at the outer boundary of the period annulus

DOI10.1007/s10884-016-9559-xzbMath1444.34055OpenAlexW2546600784MaRDI QIDQ1993993

Yanyan Li

Publication date: 6 November 2018

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

Full work available at URL: http://ddd.uab.cat/record/199343

zbMATH Keywords

criticalitybifurcationcenterChebyshev systemperiod functioncritical periodic orbit

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) Bifurcation theory for ordinary differential equations (34C23) 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

Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting ⋮ The criticality of reversible quadratic centers at the outer boundary of its period annulus ⋮ On the upper bound of the criticality of potential systems at the outer boundary using the Roussarie-Ecalle compensator ⋮ New lower bound for the number of critical periods for planar polynomial systems ⋮ The period function of reversible Lotka-Volterra quadratic centers ⋮ Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting

Cites Work

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• Monotonicity of the period of a nonlinear oscillator
• Unfoldings of saddle-nodes and their Dulac time
• Geometric methods for two-point nonlinear boundary value problems
• The problem of differentiating an asymptotic expansion in real powers. I: Unsatisfactory or partial results by classical approaches
• Bounding the number of zeros of certain abelian integrals
• The problem of differentiating an asymptotic expansion in real powers. II: Factorizational theory
• Darboux linearization and isochronous centers with a rational first integral
• Monotonicity of the first eigenvalue and the global bifurcation diagram for the branch of interior peak solutions
• The criticality of centers of potential systems at the outer boundary
• Unfolding of resonant saddles and the Dulac time
• 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
• Study of the period function of a two-parameter family of centers
• 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
• On the reversible quadratic centers with monotonic period function
• A NOTE ON THE CRITICAL PERIODS OF POTENTIAL SYSTEMS
• 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
• On the time function of the Dulac map for families of meromorphic vector fields