Singular perturbations arising in Hilbert's 16th problem for quadratic vector fields

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 78, Issue 2, 1998, Pages 133-136

  Smits, B ^a  

^a HASSELT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944442841     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/(SICI)1521-4001(199802)78:2<133::AID-ZAMM133>3.0.CO;2-M     Document Type: Article

References (13)

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3. ROUSSARIE, R.: A note on the finite cyclicity property and Hilbert's 16th problem. IN BAMON, R.; LABARCA, R.; PALIS, J. (eds.): Dynamical systems. Valparaiso 1986, Lecture Notes in Math. 1331 (1988), pp. 161-168.
4. ROUSSEAU, C.: In: Bifurcations of periodic orbits of vector fields. Nato Advanced. Studies C408, (1992), pp. 383-421.
5. MOURTADA, A.: Cyclicité finie des polycycles hyperboliques des champs de vecteurs du plan, mise sous forme normale. Lecture Notes in Mathematics 1455 (1990), pp. 272-314.
6. DUMORTIER, F.; ROUSSARIE, R.; ROUSSEAU, C.: Hilbert's 16th problem for quadratic fector fields. J. Diff. Equ. 110 (1990), 86-133.
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8. DENKOWSKA, Z.; ROUSSARIE, R.: A method of desingularization for analytic two-dimensional vector field families. Bol. Soc. Brasil. Math. 22 (1991), 93-126.
9. DUMORTIER, F.: Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations (notes written with B. SMITS). In: Bifurcations of periodic orbits of vector fields. Nato Advanced Studies C408, (1992), pp. 20-73.
10. DUMORTIER, F.; SMITS, B.: Transition time analysis with global desingularisation. Trans. Amer. Math. Soc. 347 (1995), 4129-4145.
11. SMITS, B.: Singular perturbations in quadratic vector fields. PhD thesis 1997.
12. LLIBRE, J.: Personal communication.
13. ALLEN, J. D.; O'MALLEY, R. E.: Singularly perturbed boundary value problems viewed in the Liénard plane. In WONG, R. (ed.): Asymptotic and computational analysis. Lecture Notes in Pure and Applied Math. 124 Dekker 1990, pp. 357-378.