On the time function of the Dulac map for families of meromorphic vector fields

P. Mardešić; D. Marín; J. Villadelprat

doi:https://doi.org/10.1088/0951-7715/16/3/305

On the time function of the Dulac map for families of meromorphic vector fields

P. Mardešić, D. Marín, J. Villadelprat

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

21 Citations (Scopus)

Abstract

Given an analytic family of vector fields in ℝ2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.

Original language	English
Pages (from-to)	855-881
Journal	Nonlinearity
Volume	16
DOIs	https://doi.org/10.1088/0951-7715/16/3/305
Publication status	Published - 1 May 2003

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title = "On the time function of the Dulac map for families of meromorphic vector fields",

abstract = "Given an analytic family of vector fields in ℝ2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.",

author = "P. Marde{\v s}i{\'c} and D. Mar{\'i}n and J. Villadelprat",

year = "2003",

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AU - Mardešić, P.

AU - Marín, D.

AU - Villadelprat, J.

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Y1 - 2003/5/1

N2 - Given an analytic family of vector fields in ℝ2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.

AB - Given an analytic family of vector fields in ℝ2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.

U2 - https://doi.org/10.1088/0951-7715/16/3/305

DO - https://doi.org/10.1088/0951-7715/16/3/305

M3 - Article

VL - 16

SP - 855

EP - 881

ER -