scientific article; zbMATH DE number 1330829

zbMath0994.34024MaRDI QIDQ4261270

Giuseppe Gaeta

Publication date: 13 October 2002

Full work available at URL: http://www.numdam.org/item?id=AIHPA_1999__70_6_461_0

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zbMATH Keywords

harmonic oscillatorPoincaré renormalized formsfiltered Lie algebra

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05)

Related Items (10)

POINCARé CODE: a package of open-source implements for normalization and computer algebra reduction near equilibria of coupled ordinary differential equations ⋮ Non-quadratic additional conserved quantities in Birkhoff normal forms ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ Normal form theory and spectral sequences. ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ Spectral sequences and parametric normal forms ⋮ An algorithm for computing a new normal form for dynamical systems ⋮ Chebyshev economization in Poincaré-Dulac transformations of nonlinear systems ⋮ Further reductions of normal forms for dynamical systems ⋮ Leaf-normal form classification for \(n\)-Tuple Hopf singularities

Cites Work

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• Lie-point symmetries and nonlinear dynamical systems
• On the convergence of normalizing transformations in the presence of symmetries
• On a Hilbert space of analytic functions and an associated integral transform part I
• Uniqueness and non-uniqueness of normal forms for vector fields
• Poincare normal forms and Lie point symmetries

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