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Quasi-regularity property for unfoldings of hyperbolic polycycles. (English) Zbl 0810.58028
Camacho, C. (ed.) et al., Complex analytic methods in dynamical systems. Proceedings of the congress held at Instituto de Matemática Pura e Aplicada, IMPA, Rio de Janeiro, Brazil, January 1992. Paris: Société Mathématique de France, Astérisque. 222, 303-326 (1994).
The paper, clearly connected with the Hilbert XVI-th problem, extends the result of R. Roussarie about hyperbolic loops to any 1-parameter unfoldings of hyperbolic polycycles.
The notion of quasi-regular mappings, introduced by Ilyashenko is used. The ideal of coefficients is also applied.
In fact it would be much easier for a novice reader to read first the work of R. Roussarie [Nonlinearity 2, No. 1, 73-117 (1989; Zbl 0679.58037)] as an absolutely necessary introduction and reference. The present paper is its beautiful generalization. Both co-authors are former students of R. Roussarie and have brought clearly their own credit to the paper.
For the entire collection see [Zbl 0797.00019].

MSC:
37D99 Dynamical systems with hyperbolic behavior
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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