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A general symmetry preserving reduction scheme and normal form for dynamical systems with a compact symmetry group

Maria Cristina Ciocci·Johan Noldus
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Abstract

We present a generalized Lyapunov Schmidt reduction scheme for diffeomorphisms living on a finite dimensional real vector space V which transform under real one dimensional characters of an arbitrary compact group with linear action V. Moreover we prove a normal form theorem, such that the normal form still has the desirable transformation properties with respect to the character.

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Maria Cristina Ciocci, Johan Noldus. 2004-11-23. A general symmetry preserving reduction scheme and normal form for dynamical systems with a compact symmetry group. https://arxiv.org/abs/math/0411510

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