Linearization of resonant vector fields

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...

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...

Linearization of families of germs of hyperbolic vector fields

On the index of finite determinacy of resonant vector fields

In this paper we study normal forms for a class of germs of 1-resonant vector fields on R with mutually different eigenvalues which may admit extraneous resonant relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result lead...

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