Normal Forms, symmetry, and linearization of dynamical systems
D. Bambusi, G. Cicogna, G. Gaeta, G. Marmo
TL;DR
This paper explores how symmetries can ensure the linearization of dynamical systems through Poincaré Normal Forms, addressing convergence issues and generalizations of the main results.
Contribution
It provides a formal analysis of symmetry-induced linearization and extends the results to broader classes of dynamical systems.
Findings
Symmetry guarantees perturbative linearizability.
Convergence of the linearization procedure is analyzed.
Generalizations of the main results are discussed.
Abstract
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and later pay attention to the convergence of the linearizing procedure. We also discuss some generalizations of our main result
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