Plausibilidad y demostración en el teorema de recurrencia de Poincaré
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Abstract
The aim of this paper is to show that the examples introduced to give a theorem plausibility are not affected by the historical change in conceptual frameworks and styles of mathematical practice. To illustrate this point, I use Poincaré’s recurrence theorem and its corollary, which taken together challenge and surpass the “generic reasoning” that dominated the production of theorems during the XIX century.
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Appell, Paul, 1928, Oeuvres de Henri Poincaré, Tomo I, Gauthier-Villars, París.
Arnold, Vladímir, 1989, Mathematical Methods of Classical Mechanics, Springer, Nueva York.
Aubin, David, y Amy Dahan Dalmedico, 2002, “Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolutions, Disciplines and Culture”, Historia Mathematica, vol. 29, no. 3, pp. 273–339. (https://doi.org/10.1006/hmat.2002.2351)
Bathia, N.P., y G.P. Szegö, 1970, Stability Theory of Dynamical Systems, Springer Verlag, Berlín.
Birkhoff, George D., 1927a, “Stability and the Equations of Dynamics”, Amer. Jour. Math., vol. 49, no. 1, pp. 1–38.
Birkhoff, George D., 1927b, Dynamical Systems, American Mathematical Society, Providence, Rhode Island, Estados Unidos.
Birkhoff, George D., 1912, “Quelques théorèmes sur le mouvement des systèmes dynamiques”, Bull. Soc. Math de France, vol. 40, pp. 305–323.
Bôcher, Maxime, 1900, “The Theory of Linear Dependence”, Annales of Mathematics, vol. 2, pp. 81–96.
Bromberg, Shirley, y Ernesto Pérez-Chavela Lacomba, 2014, “El error que cambió la mecánica celeste. Las vicisitudes de Poincaré”, Miscelánea Matemática, vol. 58, pp. 137–152.
Chemla, Karine, Renaud Chorlay, y David Rabouin, 2016, The Oxford Handbook of Generality in Mathematics and the Sciences, Oxford University Press, Reino Unido.
Condillac, Etienne Bonnot, 1822, La langue des calculs, Leconte et Durey, París, tomo 16 de las Obras completas.
Hadamard, Jacques, 1897, “Sur les trajectoires en dynamique”, Journal de Mathématiques, vol. 3, pp. 331–388.
Hawkins, Thomas, 2005, “Frobenius, Cartan and the Problem of Pffaf”, Arch. Hist. Exact Sci., vol. 59, no. 4, pp. 381–436.
Hawkins, Thomas, 1970, Lebesgue’s Theory of Integration, University of Wisconsin Press.
Hopf, Eberhard, 1948, Ergodentheorie, Chelsea, Nueva York.
Jaffe, Arthur, y Frank Quinn, 1993, “Theoretical Mathematics’: Toward a Cultural Synthesis of Mathematics and Theoretical Physics”, Bull. Am. Math. Soc., vol. 29, pp. 1–13.
Kurth, Rudolf, 1960, Axiomatics of Classical Statistical Mechanics, Pergamon, Reino Unido.
Kurth, Rudolf, 1957, Introduction to the Mechanics of Stellar Systems, Pergamon, Reino Unido.
Lakatos, Imre, 1976, Proofs and Refutations, Cambridge University Press, Cambridge.
Liapounoff, Alexandr, 1907, “Probléme géneral de la stabilité du mouvement”, Annales de la Faculté des Sciences de Toulouse, 2 series, vol. 9, Annals of Mathematics Studies, 1947, Princeton/Oxford.
Landau, Lev, y E.M. Lifchitz, 1971, Mécanique des fluides, Éditions Mir, Moscú.
Letellier, Christophe et al., 2021, “Some Elements for a History of Dynamical Systems Theory”, Chaos, vol. 31, no. 5, 053110.
(https://doi.org/10.1063/5.0047851)
Nemytskii, Viktor-Vladimirovich, y V.V. Stepanov, 1989, Qualitative Theory of Differential Equations, Dover, Nueva York.
Poincaré, Henry, 1905, La valeur de la science, Flammarion, París. [Versión en inglés: The Value of Science: Essential Writings of Henri Poincaré, Modern Library, Nueva York, 2001.]
Poincaré, Henry, 1899, Les méthodes nouvelles de la mécanique céleste, Tomo III, Gauthier-Villars/Dover 1957, Nueva York.
Poincaré, Henry, 1890, “Sur le problème des trois corps et les équations de la dynamique”, Acta Mathematica, vol. 13, pp. 5–270.
Poincaré, Henry, 1885, “Sur les courbes définies par les équations différentielles”, Journal de Mathématiques pures et appliquées, 4 serie, tomo 1, en Appell 1928, pp. 90–161.
Poincaré, Henry, 1882, “Mémoire sur les courbes définies par une équation différentielle”, Journal de Mathématiques, 3 serie, tomo 7, en Appell 1928, pp. 3–84.
Robadey, Anne, 2016, “Elaboration of a Statement Degree of Generality of a Property: Poincaré’s Work on the Recurrence Theorem”, en Karine Chemla et al. 2016, pp. 169–222.
Roque, Tatiana, 2011, “Stability of Trajectories from Poincaré to Birkhoff: Approaching a Qualitative Definition”, Arch. Hist. Exact Sci., vol. 65, no. 3, pp. 295–342.
Ruelle, David, 1991, Hasard et chaos, Éditions Odile Jacob, París.
Ruelle, David, y Floris Takens, 1971, “On the Nature of Turbulence”, Les Recontres Physiciens-Mathématiciens de Strasbourg RCP–25, Conferencias de Haïm Brézis, David Ruelle et Floris Takens y un texto de Rosemonde Gérard et Mme A. Sec, tomo 12, presentación no. 2, 44pp.
Saks, Stanislaw, 1937, Theory of the Integral, Hafner, Nueva York.
Sheynin, Oscar B., 1991, “H. Poincaré’s Work on Probability”, Arch. Hist. Exact Sci., vol. 42, no. 2, pp. 137–171.
Wagon, Stan, 1987, The Banach-Tarski Paradox, Cambridge University Press, Cambridge.
Wallace, David, 2015, “Recurrence Theorems: A Unified Account”, Journal of Math. Phys., vol. 56, no. 2. (https://doi.org/10.1063/1.4907384)

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