Normal forms and the problem of the center

DOI10.1016/S0007-4497(00)01070-8zbMath1182.37034MaRDI QIDQ5949429

Bertrand Schuman, Jacky Cresson

Publication date: 21 November 2001

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

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) Nonlinear first-order PDEs (35F20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10) Normal forms on manifolds (58K50)

Related Items (3)

Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat ⋮ A method for characterizing nilpotent centers ⋮ Mould calculus

Cites Work

• Unique normal forms for vector fields and Hamiltonians
• Singularities that are inaccessible by geometry
• Correction and linearization of resonant vector fields and diffeomorphisms
• The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
• Singularities of vector fields
• Formes normales et problème du centre symétrique
• Successive derivatives of a first return map, application to the study of quadratic vector fields
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