Global dynamics of the Beno?t system

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• 作者：Maurício Firmino Silva Lima (1)
  Jaume Llibre (2)
  
• 关键词：Equilibrium point ; First integral ; Invariant manifolds ; Homoclinic orbit ; Heteroclinic orbit ; Poincaré compactification ; Poincaré sphere ; Beno?t system ; 34A36 ; 34A60 ; 34C25 ; 34C37
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：193
• 期：4
• 页码：1103-1122
• 全文大小：481 KB
• 参考文献：1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. National Bureau of Standards Applied Mathematics, Series 55, (1972)
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  3. Beno?t, E.: Perturbation singulière en dimension trois: canards en un pseudo-singulier noeud. Bull. de la Société Mathématique de France 129-, 91-13 (2001)
  4. Beno?t, E., Callot, J.F., Diener, F., Diener, M.: Chasse au canard. Collectanea Math. 31-2(1-), 37-19 (1981)
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  6. Dumortier, F., Llibre, J., Artés, J.C.: Qualitative Theory of Planar Differential Systems. Universitext. Springer, Berlin (2006)
  7. Hale, J.: Ordinary Differential Equations. Robert E. Krieger Publishing Company, INC, Huntington (1980)
  8. Mishchnko, E.F., Kolesov, Yu. S., Kolesov, A. Yu., Rhozov, N. Kh.: Asymptotic methods in singularly perturbed systems. Monographs in Contemporary Mathematics; Consultants Bureau, New York, A Division of Plenum Publishing Cooperation 233 Springer Street, New York, N.Y. 10013, (1994)
  9. Szmolyan, P., Wechselberger, M.: Canards in \(\mathbb{R}^3\) . J. Diff. Eq. 177, 419-53 (2001) CrossRef
  10. Wechselberger, M.: Existence and bifurcation of canards in \(\mathbb{R}^3\) in the case of a folded node. SIAM J. Appl. Dyn. Syst. 4, 101-39 (2005) CrossRef
  
• 作者单位：Maurício Firmino Silva Lima (1)
  Jaume Llibre (2)
  
  1. Centro de Matemática Computa??o e Cogni??o, Universidade Federal do ABC, Santo André, 09210-170, S.P. Brazil
  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain
  
• ISSN：1618-1891

文摘

In this paper, we work with a two-degree polynomial differential system in \(\mathbb R ^3\) related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincaré ball using the Poincaré–Lyapunov compactification.