For an arbitrary analytic system which has a linear center
at the origin we compute recursively all its Poincare–Lyapunov
constants in terms of the coefficients of the
system, giving an answer to the classical center problem. We
also compute the coefficients of the Poincare
series in terms of the same coefficients. The algorithm for
these computations has an easy implementation. Our method does
not need the computation of any definite or indefinite integral.
We apply the algorithm to some polynomial differential
systems.
Keywords:
arbitrary analytic system which has linear center origin compute recursively its poincare lyapunov constants terms coefficients system giving answer classical center problem compute coefficients poincare series terms coefficients algorithm these computations has easy implementation method does computation definite indefinite integral apply algorithm polynomial differential systems
Affiliations des auteurs :
Jaume Giné
1
;
Xavier Santallusia
1
1
Departament de Matematica Universitat de Lleida Avda. Jaume II, 69 25001 Lleida, Spain
@article{10_4064_am28_1_2,
author = {Jaume Gin\'e and Xavier Santallusia},
title = {On the {Poincar\'e{\textendash}Lyapunov} constants
and the {Poincare} series},
journal = {Applicationes Mathematicae},
pages = {17--30},
year = {2001},
volume = {28},
number = {1},
doi = {10.4064/am28-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am28-1-2/}
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AU - Xavier Santallusia
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%A Xavier Santallusia
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and the Poincare series
%J Applicationes Mathematicae
%D 2001
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Jaume Giné; Xavier Santallusia. On the Poincaré–Lyapunov constants
and the Poincare series. Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 17-30. doi: 10.4064/am28-1-2
