Linearization of non-degenerate analytic centres in R~3

摘要

In this paper, we study the linearization problem of a non-degenerate analytic centre on a centre manifold in R~3. We show how the case of constant divergence of the associated vector field can be linearized with the help of inverse Jacobi multipliers. Moreover, we also combine methods of Lie symmetries from a given analytic commutator with linear part without resonances to get explicitly the linearizing change of variables. Finally, we show how the methods work in some examples.