Contributions to the transformation theory of dynamics
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- by Daniel C. Lewis PDF
- Trans. Amer. Math. Soc. 46 (1939), 374-388 Request permission
References
- George D. Birkhoff, Surface transformations and their dynamical applications, Acta Math. 43 (1922), no. 1, 1–119. MR 1555175, DOI 10.1007/BF02401754 —Nouvelles recherches sur les systèmes dynamiques, Memoriae Pontificiae Academiae Scientiae Novi Lyncaei, (3), vol. 1, pp. 85-216. —Dynamical Systems, American Mathematical Society Colloquium Publications, vol. 9, New York, 1927. —With D. C. Lewis, On the periodic motions near a given periodic motion of a dynamical system, Annali di Matematica, (4), vol. 12 (1933), pp. 117-133. E. Goursat Leçons sur le Problème de Pfaff, Paris, 1922. D. C. Lewis On formal power series transformations. To be published in the Duke Mathematical Journal.
- Daniel C. Lewis Jr., Invariant Manifolds Near an Invariant Point of Unstable Type, Amer. J. Math. 60 (1938), no. 3, 577–587. MR 1507339, DOI 10.2307/2371599 —The formal theory of conservative transformations in $2n$-dimensional space, Bulletin of the American Mathematical Society, abstract 41-5-197.
- Daniel C. Lewis Jr., On Certain Periodic Motions of Dynamical Systems with More than Two Degrees of Freedom, Amer. J. Math. 56 (1934), no. 1-4, 25–41. MR 1506999, DOI 10.2307/2370909 —Sulle oscillazioni periodiche d’un sistema dinamico, Rendiconti della Reale Accademia Nazionale dei Lincei, (6$^{a}$), vol. 19 (1934), pp. 234-237. C. C. MacDuffee The Theory of Matrices, Berlin, 1933. E. von Weber Vorlesungen über das Pfaff’sche Problem und die Theorie der partiellen Differentialgleichungen erster Ordnung, Leipzig, 1900. E. T. Whittaker A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 2d edition, Cambridge, 1917.
- E. R. van Kampen and Aurel Wintner, On the reduction of dynamical systems by means of parametrized invariant relations, Trans. Amer. Math. Soc. 44 (1938), no. 2, 168–195. MR 1501966, DOI 10.1090/S0002-9947-1938-1501966-6
- Aurel Wintner, Three Notes on Characteristic Exponents and Equations of Variation in Celestial Mechanics, Amer. J. Math. 53 (1931), no. 3, 605–625. MR 1506840, DOI 10.2307/2371169
Additional Information
- © Copyright 1939 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 46 (1939), 374-388
- MSC: Primary 70.1X
- DOI: https://doi.org/10.1090/S0002-9947-1939-0000743-6
- MathSciNet review: 0000743