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Successive derivatives of a first return map, application to the study of quadratic vector fields

Published online by Cambridge University Press:  19 September 2008

J. P. Francoise
J. P. Francoise
Affiliation:
Université de ParisVI, URA 213, 4, Place Jussieu, tour 46–45, 5e étage, 75252 Paris, France
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Abstract

We provide an algorithm to compute the first non-zero derivative of the return map r ↦ L(r, ε) of a planar vector field which is a polynomial perturbation of . It yields a new method for finding the centre conditions in the case of a homogeneous perturbative part.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996 , pp. 87 - 96
Copyright
Copyright © Cambridge University Press 1996

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References

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