Nguyen Tien Zung
UMR5219, Universite Toulouse 3, France
Institut de Mathematiques de Toulouse, Universite Toulouse III
Zung N., Minh T.
2013, vol. 18, no. 6, pp. 608-622
The aim of this paper is to extend the notion of commutativity of vector fields to the category of singular foliations using Nambu structures, i.e., integrable multi-vector fields. We will classify the relationship between singular foliations and Nambu structures and show some basic results about commuting Nambu structures.
Kolmogorov Condition near Hyperbolic Singularities of Integrable Hamiltonian Systems
2007, vol. 12, no. 6, pp. 680-688
In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point).