On the Poincaré-Lyapunov centre theorem

zbMath0959.34021MaRDI QIDQ1577426

Marco Brunella, Massimo Villarini

Publication date: 22 April 2001

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

zbMATH Keywords

stabilityperiodic orbitssingularities of vector fieldsanalytic multicentrecentre-type singularity of an analytic vector field on the planecomplexification of the vector fieldlinearization of compact group actionslinearization of multicentresmultirotationPoincaré-Lyapunov centre theorem

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Stability of solutions to ordinary differential equations (34D20) 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) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (3)

Smooth foliations by circles of with unbounded periods and nonlinearizable multicentres ⋮ A rigidity property of perturbations of \(n\) identical harmonic oscillators ⋮ Smooth linearization of centres

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