Formal linearization of vector fields and related cohomology. II

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

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

On the Leibniz cohomology of vector fields

I. M. Gelfand and D. B. Fuks have studied the cohomology of the Lie algebra of vector fields on a manifold. In this article, we generalize their main tools to compute the Leibniz cohomology, by extending the two spectral sequences associated to the diagonal and the order filtration. In particular, we determine some new generators for the diagonal Leibniz cohomology of the Lie algebra of vector ...

Correction and linearization of resonant vector fields and diffeomorphisms

We extend the classical Siegel-Brjuno-Rüssmann linearization theorem to the resonant case by showing that under A. D. Brjuno’s diophantine condition, any resonant local analytic vector field (resp. diffeomorphism) possesses a well-defined correction which (1) depends on the chart but, in any given chart, is unique (2) consists solely of resonant terms and (3) has the property that, when substra...

Ju l 2 00 6 GELFAND - FUCHS COHOMOLOGY OF INVARIANT FORMAL VECTOR FIELDS

Let Γ be a finite group acting linearly on a vector space V . We compute the Lie algebra cohomology of the Lie algebra of Γ-invariant formal vector fields on V . We use this computation to define characteristic classes for foliations on orbifolds.