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Non-degenerate singularities of integrable dynamical systems

Published online by Cambridge University Press:  09 October 2013

NGUYEN TIEN ZUNG
NGUYEN TIEN ZUNG*
Affiliation:
Institut de Mathématiques de Toulouse, UMR5219, Université Toulouse 3, France email tienzung.nguyen@math.univ-toulouse.fr
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Abstract

We give a natural notion of non-degeneracy for singular points of integrable non-Hamiltonian systems, and show that such non-degenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We conjecture that the same result also holds in the smooth case, and prove this conjecture for systems of type $(n, 0)$, i.e. $n$ commuting smooth vector fields on an $n$-manifold.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 994 - 1008
Copyright
© Cambridge University Press, 2013 

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