Cyclicity of elementary polycycles with fixed number of singular points in generic $k$-parameter families

DOI10.1090/S1061-0022-2011-01158-6zbMath1230.34034MaRDI QIDQ3020549

I. V. Shchurov, P. I. Kaleda

Publication date: 4 August 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

limit cyclepolycycleHilbert's sixteenth problemHilbert-Arnold's problem

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Unnamed Item

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