Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane
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Publication:1058038
DOI10.1007/BF01086157zbMath0564.34034OpenAlexW116565880MaRDI QIDQ1058038
Publication date: 1984
Published in: Functional Analysis and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01086157
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
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Asymptotic expansion of the period function. II. ⋮ On the solutions of ordinary differential equations in the form of Dulac series ⋮ Keeping track of limit cycles ⋮ Extending to the complex line Dulac’s corner maps of non-degenerate planar singularities ⋮ On a four parameter family of planar vector fields ⋮ Extended holonomy and topological invariance of vanishing holonomy group ⋮ On the Dulac's problem for piecewise analytic vector fields ⋮ Normalization of strongly hyperbolic logarithmic transseries and complex Dulac germs ⋮ Asymptotic expansion of the period function. ⋮ Multiplicity of fixed points and growth of \(\varepsilon \)-neighborhoods of orbits ⋮ Analytic normalization of analytically integrable differential systems near a periodic orbit ⋮ The theory of Khovanskii and the problem of Dulac. ⋮ The Dirichlet problem in the plane with semianalytic raw data, quasi analyticity, and o-minimal structure ⋮ Linearization of complex hyperbolic Dulac germs ⋮ Saddle quantities and applications ⋮ Stability of certain planar unbounded polycycles ⋮ A Preparation Theorem for a Class of Non-differentiable Functions with an Application to Hilbert’s 16th Problem
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