Feuilleter
no. 4
Higher order Poincaré-Pontryagin functions and iterated path integrals
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 663-682 
@article{AFST_2005_6_14_4_663_0,
     author = {Lubomir Gavrilov},
     title = {Higher order {Poincar\'e-Pontryagin} functions and iterated path integrals},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {663--682},
     year = {2005},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {4},
     doi = {10.5802/afst.1107},
     mrnumber = {2188587},
     zbl = {1104.34024},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1107/}
}
TY  - JOUR
AU  - Lubomir Gavrilov
TI  - Higher order Poincaré-Pontryagin functions and iterated path integrals
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2005
SP  - 663
EP  - 682
VL  - 14
IS  - 4
PB  - Université Paul Sabatier, Institut de Mathématiques
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1107/
DO  - 10.5802/afst.1107
LA  - en
ID  - AFST_2005_6_14_4_663_0
ER  - 
%0 Journal Article
%A Lubomir Gavrilov
%T Higher order Poincaré-Pontryagin functions and iterated path integrals
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2005
%P 663-682
%V 14
%N 4
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1107/
%R 10.5802/afst.1107
%G en
%F AFST_2005_6_14_4_663_0
Lubomir Gavrilov. Higher order Poincaré-Pontryagin functions and iterated path integrals. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 663-682. doi: 10.5802/afst.1107

[1] Arnold (V.I. ). - Geometrical methods in the theory of ordinary differential equations, Grundlehr. Math. Wiss. , vol. 250, Springer-Verlag , New York (1988). | Zbl | MR

[2] Arnold (V.I. ), Gusein-Zade (S.M.), Varchenko (A.N.). - Singularities of Differentiable Maps, vols. 1 and 2, Monographs in mathematics , Birkhäuser, Boston, 1985 and 1988.

[3] Briskin (M. ) , Yomdin ( Y.). - Tangential Hilbert problem for Abel equation , preprint, 2003.

[4] Brudnyi (A. ). - On the center problem for ordinary differential equation, arXiv:math 0301339 (2003).

[5] Chen (K.-T. ).- Algebras of iterated path integrals and fundamental groups, Trans. AMS 156, p. 359-379 (1971). | Zbl | MR

[6] Chen (K.-T. ). - Iterated Path Integrals, Bull. AMS 83 (1977) 831-879. | Zbl | MR

[7] Françoise ( J.-P.). - Successive derivatives of a first return map, application to the study of quadratic vector fields, Ergod. Theory and Dyn. Syst. 16, p. 87-96 (1996). | Zbl | MR

[8] Françoise ( J.-P. ). - Local bifurcations of limit cycles, Abel equations and Liénard systems, in Normal Forms, Bifurcations and Finitness Problems in Differential Equations, NATO Science Series II, vol. 137, 2004.

[9] Fulton (W.). - Algebraic Topology, Springer , New York, 1995. | Zbl | MR

[10] Gavrilov ( L.). - Petrov modules and zeros of Abelian integrals , Bull. Sci. Math. 122, no. 8, p. 571-584 (1998). | Zbl | MR

[11] Gavrilov (L. ) , Iliev ( I.D.). - The displacement map associated to polynomial unfoldings of planar vector fields, arXiv:math.DS/0305301 (2003).

[12] Hain (R.). - The geometry of the mixed Hodge structure on the fundamental group, Proc. of Simposia in Pure Math., 46, p. 247-282 (1987). | Zbl | MR

[13] Hain (R.). - Iterated integrals and algebraic cycles: examples and prospects. Contemporary trends in algebraic geometry and algebraic topology (Tianjin, 2000), p. 55-118, Nankai Tracts Math., 5, World Sci. Publishing, River Edge, NJ, 2002. | Zbl | MR

[14] Hall (M.). - The Theory of Groups, AMS Chelsea Publishing, 1976. | Zbl | MR

[15] Hilbert (D. ). - Mathematische probleme, Gesammelte Abhandlungen III, Springer-Verlag, Berlin, p. 403-479 (1935).

[16] Ilyashenko ( Y.S.). - Selected topics in differential equations with real and complex time, in Normal Forms, Bifurcations and Finitness Problems in Differential Equations, NATO Science Series II , vol. 137, 2004, Kluwer. preprint, 2002. | MR

[17] Jebrane ( A.), Mardesic (P.), Pelletier (M.). - A generalization of Françoise's algorithm for calculating higher order Melnikov functions , Bull. Sci. Math. 126, p. 705-732 (2002). | Zbl | MR

[18] Jebrane ( A.), Mardesic (P.), Pelletier (M.). - A note on a generalization of Franoise's algorithm for calculating higher order Melnikov function, Bull. Sci. Math. 128, p. 749-760 (2004). | Zbl | MR

[19] Parsin (A.N. ). - A generalization of the Jacobian variety , AMS Translations, Series 2, p. 187-196 (1969). | Zbl

[20] Passman (D. ). - The algebraic theory of group rings , Wiley, New York, 1977. | MR

[21] Pontryagin ( L.S.).- Über Autoschwingungssysteme, die den Hamiltonischen nahe liegen, Phys. Z. Sowjetunion 6, 25-28 (1934) | Zbl

; On dynamics systems close to Hamiltonian systems, Zh. Eksp. Teor. Fiz. 4, p. 234-238 (1934), in russian.

[22] Roussarie ( R.). - Bifurcation of planar vector fields and Hilbert's sixteenth problem, Progress in Mathematics , vol. 164, Birkhäuser Verlag , Basel (1998). | Zbl | MR

Cité par Sources :