The bifurcation set of the period function of the dehomogenized Loud's centers is bounded

DOI10.1090/S0002-9939-08-09131-4zbMath1165.34017OpenAlexW1970694037MaRDI QIDQ5448926

Francesc Mañosas, Jordi Villadelprat

Publication date: 10 March 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-08-09131-4

zbMATH Keywords

period functionreversible centerSchaaf criterium

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 (16)

The criticality of reversible quadratic centers at the outer boundary of its period annulus ⋮ Bifurcation of Critical Periods from a Quartic Isochronous Center ⋮ Perturbed rigidly isochronous centers and their critical periods ⋮ 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 ⋮ Number of Critical Periods for Perturbed Rigidly Isochronous Centers ⋮ The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one ⋮ A criticality result for polycycles in a family of quadratic reversible centers ⋮ Local bifurcation of critical periods for a class of Liénard equations ⋮ Algebraic and analytical tools for the study of the period function ⋮ Criteria to bound the number of critical periods ⋮ The period function of reversible Lotka-Volterra quadratic centers ⋮ Bifurcations of zeros in translated families of functions and applications ⋮ The period function of quadratic generalized Lotka-Volterra systems without complex invariant lines ⋮ Dulac time of a resonant saddle in the loud family ⋮ Bifurcation of critical periods of polynomial systems

Cites Work

• The period function for quadratic integrable systems with cubic orbits
• The period in the Lotka-Volterra system is monotonic
• The period function of a Hamiltonian quadratic system
• The period function for second-order quadratic ODEs is monotone
• The monotonicity of period function for the codimension four quadratic system \(Q_4\).
• The period function of the generalized Lotka-Volterra centers
• The period function of reversible quadratic centers
• On the return time function around monodromic polycycles
• On the monotonicity of the period function of a quadratic system
• The periods of the Volterra-Lotka system.
• On the reversible quadratic centers with monotonic period function
• Global behaviour of solution branches for some Neumann problems depending on one or several parameters.
• A class of Hamiltonian systems with increasing periods.
• Remarks on Periods of Planar Hamiltonian Systems
• On the time function of the Dulac map for families of meromorphic vector fields
• Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems

This page was built for publication: The bifurcation set of the period function of the dehomogenized Loud's centers is bounded