Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three

Patrick Bonckaert; Vincent Naudot

Annales de la Faculté des sciences de Toulouse : Mathématiques (2001)

  • Volume: 10, Issue: 4, page 595-617
  • ISSN: 0240-2963

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Bonckaert, Patrick, and Naudot, Vincent. "Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three." Annales de la Faculté des sciences de Toulouse : Mathématiques 10.4 (2001): 595-617. <http://eudml.org/doc/73559>.

@article{Bonckaert2001,
author = {Bonckaert, Patrick, Naudot, Vincent},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Dulac map; vector field; hyperbolic equilibrium point of saddle type; asymptotic expression},
language = {eng},
number = {4},
pages = {595-617},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three},
url = {http://eudml.org/doc/73559},
volume = {10},
year = {2001},
}

TY - JOUR
AU - Bonckaert, Patrick
AU - Naudot, Vincent
TI - Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2001
PB - UNIVERSITE PAUL SABATIER
VL - 10
IS - 4
SP - 595
EP - 617
LA - eng
KW - Dulac map; vector field; hyperbolic equilibrium point of saddle type; asymptotic expression
UR - http://eudml.org/doc/73559
ER -

References

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  5. [5] IL'YASHENKO ( Yu.S.) and Yakovenko ( S.Yu.). - Finitely-smooth normal forms of local families of diffeomorphisms and vector fields, Russian Math. Surveys, 46:1 (1991), 1-43. Zbl0744.58006MR1109035
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  8. [8] Moussu ( R.). - Développement asymptotique de l'application retour d'un polycycle. In Dynamical Systems, Valparaiso 1986, volume 1331 of Lecture Notes in Mathematics, pages 140-149. Springer-Verlag, 1988. Zbl0659.58009MR961097
  9. [9] Roussarie ( R.) On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Bras. Mat., 17:67-101, 1986. Zbl0628.34032MR901596
  10. [10] Roussarie ( R.) and Rousseau ( C.). - Almost planar homoclinic loops in R3. Journal of Differential Equations, 126:1-47, 1996. Zbl0849.34036MR1382055
  11. [11] Rychlik ( M.R.). - Lorenz attractors through Shil'nikov-type bifurcation. Part I, Ergod. Th. & Dynam. Syst.10 (1990), 793-821. Zbl0715.58027
  12. [12] Sternberg ( S.). - On the structure of local homomorphisms of euclidean n-space, I, Am. J. Math.80 (1958), 623-31. Zbl0083.31406MR96854
  13. [13] Sternberg ( S.). - On the structure of local homomorphisms of euclidean n-space, II, Am. J. Math.81 (1959), 578-605. Zbl0211.56304MR109853

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