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Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation

Eric Lombardi, Laurent Stolovitch (2010)

Annales scientifiques de l'École Normale Supérieure

In this article, we study germs of holomorphic vector fields which are “higher order” perturbations of a quasihomogeneous vector field in a neighborhood of the origin of $ℂ^{n}$ , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part $S$ which ensures that if such a perturbation of $S$ is formally conjugate to $S$ then it is also holomorphically conjugate to it. We study the normal form problem relatively to $S$ . We give a condition on $S$ that ensures that there...

Note on a local invertibility

Michal Fečkan (1996)

Mathematica Slovaca

Note on a Poincaré map

Michal Fečkan (1991)

Mathematica Slovaca

Numerical integration of differential equations in the presence of first integrals: observer method

Eric Busvelle, Rachid Kharab, A. Maciejewski, Jean-Marie Strelcyn (1994)

Applicationes Mathematicae

We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum...

Displaying 1 – 4 of 4

Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation

Note on a local invertibility

Note on a Poincaré map

Numerical integration of differential equations in the presence of first integrals: observer method

Currently displaying 1 – 4 of 4