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Differential Equations and Dynamical Systems

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Abstract

Henri Poincaré presented his thesis to the Faculté des Sciences of the University of Paris to obtain the degree of doctor of mathematical sciences. The title: “Sur les propriétés des fonctions définies par les équations aux différences partielles.” It was accepted on August 1, 1879, by a committee consisting of J.-C. Bouquet (chairman), P.-O. Bonnet, and G. Darboux. The text is reproduced in [Poincaré 1916, Vol. 1].

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References

  1. V.I. Arnold, Mathematical Methods of Classical Mechanics. New York: Springer-Verlag, 1978.

    MATH  Google Scholar 

  2. V.I. Arnold, V.V. Kozlov, and A.I. Neihstadt, editors. “Mathematical aspects of classical and celestial mechanics.” In Dynamical Systems III, edited by V.I. Arnold, Encyclopaedia of Mathematical Sciences. Berlin: Springer, 1988.

    Google Scholar 

  3. June Barrow-Green. Poincaré and the Three Body Problem, History of Mathematics 11. Providence: American Mathematical Society, and London: London Mathematical Society, 1997.

    Google Scholar 

  4. G. Benettin, G. Ferrari, L. Galgani, and A. Giorgilli. “An extension of the Poincaré–Fermi theorem on the nonexistence of invariant manifolds in nearly integrable Hamiltonian systems.” Il Nuovo Cimento 72B (1982), 137–148.

    MathSciNet  Google Scholar 

  5. G.D. Birkhoff. “Proof of Poincaré’s geometric theorem.” Trans. AMS 14 (1913), 14–22.

    MathSciNet  MATH  Google Scholar 

  6. G.D. Birkhoff. “On the periodic motions of dynamical systems.” Acta Mathematica 50 (1927), 359–379.

    Article  MathSciNet  MATH  Google Scholar 

  7. Émile Borel. Introduction géométrique à quelques théories physiques. Paris: Gauthier-Villars, 1914.

    Google Scholar 

  8. Aline Boutroux. Vingt ans de ma vie, simple vérité. Nancy: Archives B Centre d’Études et de Recherches Henri Poincaré, 1912.

    Google Scholar 

  9. P. Boutroux. “Lettre de Pierre Boutroux à M. Mittag-Leffler.” Acta Math. 38 (1921), 197–201.

    Article  MathSciNet  Google Scholar 

  10. C. Briot and T. Bouquet. “Recherches sur les propriétés des fonctions définies par les équations différentielles.” J. de l’École Polytechnique, Cahier 21 (1856), 133–198.

    Google Scholar 

  11. H.W. Broer. “KAM theory: the legacy of Kolmogorov’s 1954 paper.” Bull. AMS 41 (2004), 507–521.

    Article  MathSciNet  MATH  Google Scholar 

  12. H. Bruns. “Über die Integrale des Vielkörper-Problems.” Acta Mathematica 11 (1888), 25–96.

    Article  MathSciNet  Google Scholar 

  13. Élie Cartan. Leçons sur les invariants intégraux. Paris: Hermann, 1922.

    Google Scholar 

  14. C. Chicone, Ordinary Differential Equations with Applications, Texts in Applied Mathematics 34. New York: Springer, 1999.

    Google Scholar 

  15. Willem de Sitter. “On the libration of the three inner large satellites of Jupiter.” Publ. Astr. Lab. Groningen 17 (1907), 1–119, 1907 (see also Ann. Sterrewacht Leiden vol. 12, 1925).

    Google Scholar 

  16. E. Fermi. “Generalizzazione del teorema di Poincaré sopra la non esistenza di integrali uniformi di un sistema di equazioni canoniche normali.” Il Nuovo Cimento 26 (1923), 105–115.

    Article  Google Scholar 

  17. E. Ghys. “Variations on Poincaré’s recurrence theorem.” In The Scientific Legacy of Poincaré, edited by E. Charpentier, E. Ghys, and A. Lesne, History of mathematics 36, pp. 193–206. Providence: AMS, 2010.

    Google Scholar 

  18. J.K. Hale. Ordinary Differential Equations. New York: Wiley-Interscience, 1969.

    MATH  Google Scholar 

  19. V.V. Kozlov. Symmetries, Topology and Resonances in Hamiltonian Mechanics, Ergebnisse der Mathematik und ihre Grenzgebiete 31. New York: Springer, 1996.

    Google Scholar 

  20. Émile Picard. Traité d’Analyse, 3 vols. Paris: Gauthier-Villars, 1891, 1893, 1896.

    MathSciNet  Google Scholar 

  21. Henri Poincaré. “Note sur les propriétés des fonctions définies par les équations différentielles.” J. de l’École Polytechnique, Cahier 45 (1878), 13–26; also in [Poincaré 1916] vol. 1, pp. XXXVI–XLVIII.

    Google Scholar 

  22. Henri Poincaré. “Mémoire sur les courbes définies par une équation différentielle.” J. de Mathématiques, 3e série vol. 7 (1881), 375–422, vol. 8 (1882), pp. 251–296.

    Google Scholar 

  23. Henri Poincaré. “Sur les intégrales irrégulières des équations linéraires.” Acta Mathematica 8 (1886), 295–344.

    Article  MathSciNet  MATH  Google Scholar 

  24. Henri Poincaré. “Sur le problème des trois corps et les équations de la dynamique.” Acta Mathematica 13 (1890), 1–270; also in [Poincaré 1916] vol. 7, pp. 262–479.

    Google Scholar 

  25. Henri Poincaré. Les Méthodes Nouvelles de la Mécanique Céleste, 3 vols. Paris: Gauthier-Villars, 1892, 1893, 1899.

    Google Scholar 

  26. Henri Poincaré. “Conférence sur la télégraphique sans fil.” Revue d’électricité (27 Décembre 1908), 387–393.

    Google Scholar 

  27. Henri Poincaré, Sur un théorème de géometrie, Rend. Circolo Mat. Palermo 33, pp. 375-407, 1912; also in [Poincaré 1916], vol. 6, pp. 499–538.

    Google Scholar 

  28. Henri Poincaré, Oeuvres de Henri Poincaré publiées sous les auspices de l’Académie des Sciences, vols. 1–12, Gauthier-Villars, Paris, 1916–1954.

    Google Scholar 

  29. Henri Poincaré and Gösta Mittag-Leffler. La correspondance entre Henri Poincaré et Gösta Mittag-Leffler, avec en annexes les lettres échangées par Poincaré avec Fredholm, Gyldén et Phragmén; presentée et annotée par Philippe Nabonnand. Basel: Birkhäuser, 1999.

    Google Scholar 

  30. Henri Poincaré. Correspondence Archives Henri Poincaré, Université de Nancy.

    Google Scholar 

  31. J.A. Sanders, F. Verhulst, and J. Murdock. Averaging Methods in Nonlinear Dynamical Systems, second revised edition, Applied Math. Sciences 59. New York: Springer, 2007.

    Google Scholar 

  32. C.L. Siegel and J.K. Moser. Lectures on Celestial Mechanics, Grundlehren der mathematischen Wissenschaften 187. New York: Springer, 1971.

    Google Scholar 

  33. S. Smale. “Differentiable dynamical systems.” Bull. AMS 73 (1967) 747–817.

    Article  MathSciNet  MATH  Google Scholar 

  34. V.S. Steckline. “Zermelo, Boltzmann and the recurrence paradox.” Am. J. Physics 51(1983), 894–897.

    Article  Google Scholar 

  35. T.-J. Stieltjes. “Recherches sur quelques séries semi-convergentes.” Ann. Scientifiques de École Normale Supérieure 3 (1886), 201–258.

    MathSciNet  MATH  Google Scholar 

  36. Félix Tisserand. Traité de mécanique céleste, 4 vols. Paris: Gauthier-Villars, 1889–1896.

    Google Scholar 

  37. E. Toulouse. Henri Poincaré. Paris: Flammarion, 1910.

    Google Scholar 

  38. E. Van der Aa and M. De Winkel. “Hamiltonian systems in 1 : 2 : ω (ω = 5 or 6) resonance.” Int. J. Nonlin. Mech. 29 (1994) 261–270.

    Article  MATH  Google Scholar 

  39. Ferdinand Verhulst. Nonlinear Differential Equations and Dynamical Systems, second revised edition. New York: Springer, 2000.

    Google Scholar 

  40. Ferdinand Verhulst. Methods and Applications of Singular Perturbations. New York: Springer, 2005.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisch Instituut, University of Utrecht, Budapestlaan 6, Utrecht, Netherlands

    Ferdinand Verhulst

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  1. Ferdinand Verhulst
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Verhulst, F. (2012). Differential Equations and Dynamical Systems. In: Henri Poincaré. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-2407-9_9

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