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Further Reductions of Normal Forms for Dynamical Systems
Journal of Differential Equations, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Guoting, Della Dora, Jean
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Normal forms, symmetry and linearization of dynamical systems [PDF]
Journal of Physics A: Mathematical and General, 1998 19 pages, no ...
Dario Bambusi +3 more
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An Algorithm for Computing a New Normal Form for Dynamical Systems
Journal of Symbolic Computation, 2000 Autonomous dynamical systems \(\dot{x}=F(x)\) are considered, with \(x\in \mathbb{R}^n\), \(F(x)\) is a vector whose components are formal power series and \(F(0)=0\). A new formal normal form for system (1) is proposed which improves the classical normal forms in the sense that it is a further reduction of the classical normal forms.
Guoting Chen, Jean Della Dora
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Geometry of Normal Forms for Dynamical Systems [PDF]
Nonlinear Systems and Their Remarkable Mathematical Structures, 2018 We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting based on the action of certain groups.
Giuseppe Gaeta
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Systematic derivation of amplitude equations and normal forms for dynamical systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1998 We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from ...
Ipsen, M. +2 more
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Symmetries of dynamical systems and convergent normal forms [PDF]
Journal of Physics A: Mathematical and General, 1995 It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical system) into normal ...
G Cicogna
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Formal equivalence between normal forms of reversible and hamiltonian dynamical systems [PDF]
Communications on Pure and Applied Analysis, 2014 We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.
Ricardo Miranda Martins
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Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms [PDF]
Journal of Differential Equations, 2016 We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the ...
Márcio R.A. Gouveia +3 more
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Normal forms for the Laplace resonance [PDF]
Celestial mechanics & dynamical astronomy, 2021 We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second order in the ...
Pucacco, Giuseppe, Pucacco, G
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Convergent normal forms of symmetric dynamical systems [PDF]
Journal of Physics A: Mathematical and General, 1997 It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian) dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical sytem (or vector field) into Poincaré-Dulac normal form.
G. Cicogna
openaire +6 more sources