Sur quelques problèmes de la théorie des systèmes dynamiques
Vladimir I. Arnold1
1 Université de Paris-Dauphine Place du Maréchal de Lattre de Tassigny, 75755 Paris cedex 16, France
Journées mathématiques X-UPS, Aspects des systèmes dynamiques (des équations différentielles aux itérations de fonctions) (1994), pp. 1-20.
Publié le :
DOI : 10.5802/xups.1994-01
Vladimir I. Arnold 1

1 Université de Paris-Dauphine Place du Maréchal de Lattre de Tassigny, 75755 Paris cedex 16, France 
@incollection{XUPS_1994____1_0,
     author = {Vladimir I. Arnold},
     title = {Sur quelques probl\`emes de la th\'eorie des syst\`emes dynamiques},
     booktitle = {Aspects des syst\`emes dynamiques (des \'equations diff\'erentielles aux it\'erations de fonctions)},
     series = {Journ\'ees math\'ematiques X-UPS},
     pages = {1--20},
     publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique},
     year = {1994},
     doi = {10.5802/xups.1994-01},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-01/}
}
TY  - JOUR
AU  - Vladimir I. Arnold
TI  - Sur quelques problèmes de la théorie des systèmes dynamiques
JO  - Journées mathématiques X-UPS
PY  - 1994
SP  - 1
EP  - 20
PB  - Les Éditions de l’École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-01/
DO  - 10.5802/xups.1994-01
LA  - fr
ID  - XUPS_1994____1_0
ER  - 
%0 Journal Article
%A Vladimir I. Arnold
%T Sur quelques problèmes de la théorie des systèmes dynamiques
%J Journées mathématiques X-UPS
%D 1994
%P 1-20
%I Les Éditions de l’École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-01/
%R 10.5802/xups.1994-01
%G fr
%F XUPS_1994____1_0
Vladimir I. Arnold. Sur quelques problèmes de la théorie des systèmes dynamiques. Journées mathématiques X-UPS, Aspects des systèmes dynamiques (des équations différentielles aux itérations de fonctions) (1994), pp. 1-20. doi : 10.5802/xups.1994-01. https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-01/

[1] V. I. Arnold Notes on singularities of finite codimension in the complex dynamical systems, Funct. Anal. and Appl., Volume 3 (1969) no. 1, pp. 1-6 | DOI | Zbl

[2] V. I. Arnold Local problems of analysis, Vestnik Mosk. Univ. Ser. 1, Math. Mech., Volume 25 (1970) no. 2, pp. 52-56 | MR

[3] V. I. Arnold Mathematical developments arising from Hilbert’s problems (Proc. Symp. in Pure Math.), Volume 28, American Mathematical Society, Providence, RI, 1974, p. 59

[4] V. I. Arnold Bifurcations of invariant manifolds of differential equations and structure of the neighborhood of an elliptic curve on a complex surface, Funct. Anal. and Appl., Volume 10 (1975) no. 4, pp. 1-12

[5] V. I. Arnold Geometrical methods in the theory of ordinary differential equations, Springer, New-York, 1983

[6] V. I. Arnold Sturm theorems and symplectic geometry, Funct. Anal. and Appl., Volume 19 (1985) no. 4, pp. 1-10 | MR

[7] V. I. Arnold Dynamics of complexity of intersections, Boletim da Sociedade Brasiliera de Mathematica, Volume 21 (1990) no. 1, pp. 1-10 | DOI | MR | Zbl

[8] V. I. Arnold Dynamics of intersections, Analysis etc, Research papers published in honor of Jürgen Moser’s 60th Birthday (P. Rabinovitz; E. Zehnder, eds.), Academic Press, San Diego, 1990, pp. 77-84

[9] V. I. Arnold Topological and ergodic properties of closed differential 1-forms, Funct. Anal. Appl, Volume 25 (1991) no. 2, pp. 1-12

[10] V. I. Arnold Polyintegrable flows, Algebra and Analysis (St. Petersbourg Math. J.), Volume 4 (1992) no. 6, pp. 54-62 | Zbl

[11] V. I. Arnold Majoration of Milnor numbers of intersections in holomorphic dynamical systems, Topological Methods in Modern Mathematics, J.W. Milnor’s Jubiley volume, Publish or Perish, Houston, 1993, pp. 379-390 | Zbl

[12] V. I. Arnold Problems on singularities and dynamical systems, Developments in mathematics : the Moscow school, Chapman & Hall, London, 1993, pp. 251-274 | Zbl

[13] M. Artin; B. Mazur On periodic points, Annals of Mathematics, Volume 81 (1965), pp. 82-99 | DOI | Zbl

[14] S. S. Chern; R. Lashof On the total curvature of immersed manifolds, Amer. Math. J., Volume 79 (1957), pp. 306-318 & Michigan Math. J. 5 (1958), 5–12 | DOI | MR | Zbl

[15] D. Fried Periodic points of holomorphic maps, Topology, Volume 25 (1986) no. 4, pp. 429-441 | DOI | MR | Zbl

[16] A. B. Givental Sturm theorems for hyperelliptic integrals, Algebra and Analysis, Volume 1 (1989) no. 5, pp. 95-102 (traduction anglaise : Leningrad Math. J. 1 :5 (1990), p. 1157–1163) | Zbl

[17] E. Gonzales-Rosales On the growth of the number of periodic points of dynamical systems, Funct. Anal., Volume 25 (1991) no. 4, pp. 14-22 & 26 (1992), no. 2, p. 29-35

[18] M. Herman Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES, Volume 49 (1979), pp. 5-233 | DOI | Numdam | Zbl

[19] A. G. Khovanskiï Real analytic manifolds with the property of finiteness and complex abelian integrals, Funct. Anal. and Appl., Volume 18 (1984) no. 2, pp. 40-50 | MR

[20] A. N. Kolmogorov On dynamical systems with integral invariant on the torus, Dokl. Akad. Nauk SSSR, Volume 93 (1953) no. 5, pp. 763-766 (en russe, traduction anglaise dans : A.N. Kolmogorov, Selected Papers Vol. 1, Mathematics and Mechanics (V.M. Tikhomirov Editor), Kluwer, Dordrecht (1991), 344–348) | MR | Zbl

[21] A. N. Kolmogorov General theory of dynamical systems and classical mechanics, Proc. Int. Congr. Math. (1954) Amsterdam, Volume 1, 1957, pp. 315-333 (en russe, traduction anglaise dans : A.N. Kolmogorov, Selected Papers Vol. 1, Mathematics and Mechanics (V.M. Tikhomirov Editor), Kluwer, Dordrecht (1991), 355-374) | Zbl

[22] O. S. Kozlovski The dynamics of intersections of analytic manifolds, Russian Acad. of Sciences Doklady, Volume 45 (1992) no. 2, pp. 425-427

[23] S. P. Novikov Quasiperiodic structures in topology, Topological Methods in Modern Mathematics, J.W. Milnor’s Jubiley volume, Publish or Perish, Houston, 1993, pp. 223-234 | MR | Zbl

[24] G. S. Petrov The number of zeros of complete elliptic integrals, Funct. Anal. and Appl., Volume 18 (1984) no. 2, pp. 73-74 & 20 (1986), no. 1, p. 46–49 ; 22 (1988), no. 1, p. 83–84 ; 23 (1989), no. 2, p. 88–89 ; 24 (1990), no. 3, p. 45–50 ; Mat. Zametki 44 (1988), no. 3, p. 393–401 | MR

[25] M. Shub; D. Sullivan A remark on the Lefschetz fixed points formula for differentiable maps, Topology, Volume 13 (1974), pp. 189-191 | DOI | MR | Zbl

[26] A. N. Varchenko Estimation of the number of zeros of an abelian integral depending on a parameter and limit cycles, Funct. Anal. and Appl., Volume 18 (1984) no. 2, pp. 14-25 | MR

Cité par Sources :