Abstract
Padé approximants (P.A.) have been recently used to explore the singularity structure of the normalizing transformations of hamiltonian maps. We report here on a systematic investigation based on P.A. to detect the singularities of the analytic diffeomorphisms which linearize a polynomial map. Extended precision algorithms were used to compute high order P.A. (200 decimal digits for [100/100] P.A.), in order to check the stability of the results and to avoid the presence of poles and zeroes on the convergence circle or within it due to the noise introduced by round off.
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© 1994 Springer Science+Business Media Dordrecht
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Billi, L., Turchetti, G. (1994). Linearization of Polynomial Maps and Singularity Analysis With Extended Precision Padé Approximants. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_19
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DOI: https://doi.org/10.1007/978-94-011-0970-3_19
Publisher Name: Springer, Dordrecht
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