Vector fields near a generic submanifold

Formal Linearization of Lie Algebras of Vector Fields near an Invariant Submanifold*

Renormalisation of vector fields for a generic frequency vector

We construct a rigorous renormalisation scheme for analytic vector fields on T. We show that iterating this procedure there is convergence to a limit set with a “Gauss map” dynamics on it. This is valid for diophantine frequency vectors.

Skew-symmetric vector fields on a CR-submanifold of a para-Kählerian manifold

We deal with a CR-submanifold M of a para-Kählerian manifold M, which carries a J-skew-symmetric vector field X. It is shown that X defines a global Hamiltonian of the symplectic form Ω on M and JX is a relative infinitesimal automorphism of Ω. Other geometric properties are given. 1. Introduction. CR-submanifolds M of some pseudo-Riemannian manifolds M have been first investigated by Rosca [10...

Global Classification of Generic Multi-vector Fields of Top Degree

For any compact oriented manifold M , we show that that the top degree multi-vector fields transverse to the zero section of ∧TM are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its zero locus and a finite number of numerical invariants. The group governing the infinitesimal deformations of such multi-vector fields is computed, and an e...

Saari’s Conjecture Is True for Generic Vector Fields

The simplest non-collision solutions of the N-body problem are the “relative equilibria”, in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the moment of inertia of such a solution is constant. In 1970, D. Saari conjectured that the converse is also true for the planar Newtonian N-body problem: relative...