On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system

DOI10.1007/s10114-015-2117-3zbMath1351.34035OpenAlexW2183441907MaRDI QIDQ889458

Xian Bo Sun, Mao'an Han

Publication date: 6 November 2015

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-015-2117-3

zbMATH Keywords

limit cycleHopf bifurcationheteroclinic loopnear-Hamiltonian system\(\mathbb{Z}_4\)-equivariance

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) 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)

Related Items (7)

Simultaneity of centres in ℤ _q -equivariant systems ⋮ Counting configurations of limit cycles and centers ⋮ Limit Cycles for a Class of Zp-Equivariant Differential Systems ⋮ Lower bounds for the Hilbert number of polynomial systems ⋮ New lower bounds for the Hilbert numbers using reversible centers ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle ⋮ Symbolic computation for the qualitative theory of differential equations

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