Geodesic
On the Poincaré–Lyapunov constants and the Poincare series
Jaume Giné 1   ; Xavier Santallusia 1
1 Departament de Matematica Universitat de Lleida Avda. Jaume II, 69 25001 Lleida, Spain
Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 17-30 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am28-1-2
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

Jaume Giné  1   ; Xavier Santallusia  1

1 Departament de Matematica Universitat de Lleida Avda. Jaume II, 69 25001 Lleida, Spain 
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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

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