QUASI-CONSERVATIVE MAPS AND NORMAL FORMS FOR UNSTABLE FIXED-POINTS

The real eigenvalues lambda(1) and lambda(2) of an unstable fixed poin t of a plane diffeomorphism are resonant when lambda(j) = lambda(1)(n) lambda(2)(m). To avoid the presence of dense resonances in a one-para meter family of maps we propose a generalisation of the Birkhoff norma l form for quasi-conservative maps. This generalisation does not conve rge on the resonances but even there it can be taken as an excellent a pproximation. We use it to calculate homoclinic points with great prec ision.