41 citations · 164 across the 26 of their papers we have counts for
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Convergence of normal form transformations: The role of symmetries
G. Cicogna, S. Walcher
We discuss the convergence problem for coordinate transformations which take a given vector field into Poincaré-Dulac normal form. We show that the presence of linear or nonlinear…
Dynamical systems and σ-symmetries
Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher
A deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened "σ-prolongat…
A generalization of λ-symmetry reduction for systems of ODEs: σ-symmetries
Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher
We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the…
Orbital reducibility and a generalization of lambda symmetries
Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation bet…
Dimension increase and splitting for Poincare'-Dulac normal forms
G. Gaeta, S. Walcher
Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kosta…
Linear Lie algebras with finite dimensional centralizers
G. Gaeta, S. Walcher
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative in…