@article{AFST_2001_6_10_4_595_0,
author = {Patrick Bonckaert and Vincent Naudot},
title = {Asymptotic properties of the {Dulac} map near a hyperbolic saddle in dimension three},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {595--617},
publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
address = {Toulouse},
volume = {Ser. 6, 10},
number = {4},
year = {2001},
zbl = {1017.37009},
mrnumber = {1944252},
language = {en},
url = {https://afst.centre-mersenne.org/item/AFST_2001_6_10_4_595_0/}
}
TY - JOUR AU - Patrick Bonckaert AU - Vincent Naudot 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 SP - 595 EP - 617 VL - 10 IS - 4 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2001_6_10_4_595_0/ LA - en ID - AFST_2001_6_10_4_595_0 ER -
%0 Journal Article %A Patrick Bonckaert %A Vincent Naudot %T Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2001 %P 595-617 %V 10 %N 4 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2001_6_10_4_595_0/ %G en %F AFST_2001_6_10_4_595_0
Patrick Bonckaert; Vincent Naudot. Asymptotic properties of the Dulac map near a hyperbolic saddle in dimension three. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 4, pp. 595-617. https://afst.centre-mersenne.org/item/AFST_2001_6_10_4_595_0/
[1] ). - On the continuous dependence of the smooth change of coordinates in parametrized normal forms theorems, Journ. Diff. Eq. 106 (1993), 107-120. | MR | Zbl
[2] ). - Conjugacy of vector fields respecting additional properties, Journal of Dynamical and Control Systems 3(1997),pp. 419-432. | MR | Zbl
[3] ) and ). - On the saddle loop bifurcation. In Bifurcations of planar vector fields, proceedings Luminy 1989, volume 1455 of Lecture Notes in Mathematics, pages 44-73. Springer-Verlag, 1990. | MR | Zbl
[4] ) and ). - Finite cyclicity of elementary polycycles. In Y. Ilyashenko and S. Yakovenko, editors, Concerning the Hilbert 16th Problem volume 165 of American Mathematical Society Translations Series 2, pages 21-95. American Mathematical Society, 1995. | MR | Zbl
[5] ) and ). - Finitely-smooth normal forms of local families of diffeomorphisms and vector fields, Russian Math. Surveys, 46:1 (1991), 1-43. | MR | Zbl
[6] ), ), ). - "Homoclinic doubling cascades", "Archive for Rational Mechanics and Analysis", 160:3 (2001), 195-244. | MR | Zbl
[7] ). - Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale. In Bifurcations of planar vector fields, proceedings Luminy 1989, volume 1455 of Lecture Notes in Mathematics, pages 272-314. Springer-Verlag, 1990. | MR | Zbl
[8] ). - 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. | MR | Zbl
[9] ) 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. | MR | Zbl
[10] ) and ). - Almost planar homoclinic loops in R3. Journal of Differential Equations, 126:1-47, 1996. | MR | Zbl
[11] ). - Lorenz attractors through Shil'nikov-type bifurcation. Part I, Ergod. Th. & Dynam. Syst. 10 (1990), 793-821. | Zbl
[12] ). - On the structure of local homomorphisms of euclidean n-space, I, Am. J. Math. 80 (1958), 623-31. | MR | Zbl
[13] ). - On the structure of local homomorphisms of euclidean n-space, II, Am. J. Math. 81 (1959), 578-605. | MR | Zbl