A Quartic System with Twenty-Six Limit Cycles

DOI10.1080/10586458.2011.565252zbMath1267.34059OpenAlexW1967788039MaRDI QIDQ4915395

Tomas Johnson

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1317924424

zbMATH Keywords

interval analysisbifurcationlimit cyclepseudo-abelian integral

Mathematics Subject Classification ID

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Algorithms with automatic result verification (65G20) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (5)

Counting configurations of limit cycles and centers ⋮ Weak-foci of high order and cyclicity ⋮ A certificate-based approach to formally verified approximations ⋮ Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields ⋮ New lower bounds for the Hilbert numbers using reversible centers

Cites Work

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• A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five

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