Dynamics of commuting systems on two-dimensional manifolds

DOI10.1007/BF01783469zbMath0941.34018MaRDI QIDQ1817928

Sabatini, Marco

Publication date: 4 January 2000

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

centerspherecritical pointtorusattractionflowsvector fieldsplanar autonomous systemsnoncritical points

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Ordinary differential equations and systems on manifolds (34C40)

Related Items (9)

Complete integrability beyond Liouville-Arnol'd ⋮ From an iteration formula to Poincaré’s Isochronous Center Theorem for holomorphic vector fields ⋮ On commuting vector fields and Darboux functions for planar differential equations ⋮ Isochronous Foci for Analytic Differential Systems ⋮ Linearizability and integrability of vector fields via commutation ⋮ Non-periodic isochronous oscillations in plane differential systems ⋮ Geometry of nondegenerate \({\mathbb R}^n\)-actions on \(n\)-manifolds ⋮ ISOCHRONOUS SECTIONS VIA NORMALIZERS ⋮ Fixed point indices and invariant periodic sets of holomorphic systems

Cites Work

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• A characterization of centres via first integrals
• Liapunov direct method in approaching bifurcation problems
• Characterizing isochronous centres by Lie brackets
• Parallel dynamical systems
• Limit-cycles and rotated vector fields
• Bifurcation of Critical Periods for Plane Vector Fields
• regularity properties of the period function near a center of a planar vector field
• A connection between isochronous Hamiltonian centres and the Jacobian Conjecture

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