Non-accumulation of critical points of the Poincaré time on hyperbolic polycycles

DOI10.1090/S0002-9939-07-09026-0zbMath1127.34017MaRDI QIDQ5295110

Mariana Saavedra, Pavao Mardešić

Publication date: 27 July 2007

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

zbMATH Keywords

finitenesspolycyclepolynomial vector fieldscritical periodquasi-analyticityDulac problemnon-accumulation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting ⋮ Extending to the complex line Dulac’s corner maps of non-degenerate planar singularities ⋮ The criticality of reversible quadratic centers at the outer boundary of its period annulus ⋮ The period function of Hamiltonian systems with separable variables ⋮ On volume preserving almost Anosov flows ⋮ The criticality of centers of potential systems at the outer boundary

Cites Work

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• Asymptotic expansion of the period function. II.
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Asymptotic expansion of the period function.
• Finiteness for critical periods of planar analytic vector fields
• Finiteness theorems for limit cycles

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