AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7-Reference-Cited by-同舟云学术

AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7

Published:2010-05 Issue:05 Volume:20 Page:1451-1458
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

JOHNSON TOMAS¹,TUCKER WARWICK¹

Affiliation:

1. Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

Abstract

The limit cycle bifurcations of a Z2 equivariant planar Hamiltonian vector field of degree 7 under Z2 equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert's 16th problem for degree 7, i.e. on the possible number of limit cycles that can bifurcate from a degree 7 planar Hamiltonian system under degree 7 perturbation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127410026599

Reference24 articles.

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2. Advanced Courses in Mathematics;Christopher C.,2007

3. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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