The inner equation for generic analytic unfoldings of the Hopf-zero singularity

DOI10.3934/dcdsb.2008.10.323zbMath1162.34033OpenAlexW2317256662MaRDI QIDQ950588

B. E. Eshmatov

Publication date: 30 October 2008

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2008.10.323

zbMATH Keywords

inner systemunfoldings of Hopf-zero singularity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (16)

Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. I ⋮ Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity ⋮ Global dynamical aspects of a generalized Chen-Wang differential system ⋮ Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. II: The generic case ⋮ Breakdown of homoclinic orbits to \(L_3\) in the RPC3BP. I: Complex singularities and the inner equation ⋮ Zero-Hopf bifurcation in a Chua system ⋮ Exponentially small splitting for the pendulum: A classical problem revisited ⋮ The dud canard: existence of strong canard cycles in \(\mathbb{R}^3\) ⋮ Breakdown of homoclinic orbits to \(L_3\) in the RPC3BP. II: An asymptotic formula ⋮ Analytic invariants for the \(1 : - 1\) resonance ⋮ Zero-Hopf bifurcation in the generalized Michelson system ⋮ Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results ⋮ Zero-Hopf bifurcation in the FitzHugh-Nagumo system ⋮ The integrability and the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems ⋮ On the integrability and the zero-Hopf bifurcation of a Chen-Wang differential system ⋮ Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the Stokes constant

This page was built for publication: The inner equation for generic analytic unfoldings of the Hopf-zero singularity