Periodic orbits and non-existence of \(C^1\) first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in \(\mathbb{R}^4\)

DOI10.1007/S12215-024-01074-8MaRDI QIDQ6645845

Jaume Llibre, Renhao Tian

Publication date: 29 November 2024

Published in: Rendiconti del Circolo Matematico di Palermo (Search for Journal in Brave)

zbMATH Keywords

periodic orbitszero-Hopf bifurcationanalytic differential systemscharacteristic multipliersnon-existence of \(C^1\) first integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Cites Work

• Integrability of dynamical systems: algebra and analysis
• Limit cycles of cubic polynomial vector fields via the averaging theory
• A new result on averaging theory for a class of discontinuous planar differential systems with applications
• On the birth of limit cycles for non-smooth dynamical systems
• Averaging theory at any order for computing periodic orbits
• Averaging theory for discontinuous piecewise differential systems
• Averaging methods of arbitrary order, periodic solutions and integrability
• Nonintegrability of dynamical systems near degenerate equilibria
• On theC¹non-integrability of differential systems via periodic orbits
• The zero-Hopf bifurcations of a four-dimensional hyperchaotic system
• Higher order averaging theory for finding periodic solutions via Brouwer degree
• Nonintegrability of truncated Poincaré-Dulac normal forms of resonance degree two

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