Duke Mathematical Journal

On the finite cyclicity of open period annuli

Lubomir Gavrilov and Dmitry Novikov

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Let Π be an open, relatively compact period annulus of real analytic vector field X0 on an analytic surface. We prove that the maximal number of limit cycles which bifurcate from Π under a given multiparameter analytic deformation Xλ of X0 is finite provided that X0 is either a Hamiltonian or generic Darbouxian vector field

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Duke Math. J., Volume 152, Number 1 (2010), 1-26.

First available in Project Euclid: 11 March 2010

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Zentralblatt MATH identifier

Primary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory


Gavrilov, Lubomir; Novikov, Dmitry. On the finite cyclicity of open period annuli. Duke Math. J. 152 (2010), no. 1, 1--26. doi:10.1215/00127094-2010-005. https://projecteuclid.org/euclid.dmj/1268317522

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