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Bibliography
Abraham, R., & J. Marsden [1], Foundations of Mechanics. New York: Benjamin 1967.
Abraham, R. [2], Lectures of Smale on Differential Topology (mimeographed).
Abraham, R., & J. Robbin [3], Transversal Mappings and Flows. New York: Benjamin 1967.
Arnold, V. [1], Sur la Géométrie Différentielle des Groupes de Lie de Dimension Infinie et ses Applications à l'hydrodynamique de Fluides Parfaits. Ann. de l'Inst. Fourier; Grenoble XVI (1966).
Browder, F. [1], Non-linear equations of evolution. Ann. of Math. 80, 485 (1964).
Browder, F. [2], Non-linear initial value problems. Ann. of Math. 82, 51 (1965).
Cook, J. [1], Complex Hilbertian structures on stable linear dynamical systems. Jour. Math. Mech. 16, 339 (1966).
Derguzov, V.I., & V.A. Jakubovic [1], Existence of solutions of linear Hamiltonian equations with unbounded operator coefficients. Sov. Math. Dokl. 4, 1169 (1963).
Dieudonné, J. [1], Foundations of Modern Analysis. New York: Academic Press 1960.
Dunford, N., & J. Schwartz [1], Linear Operators (I, II). New York: Wiley 1963.
Edelen, D. [1], The invariance group for Hamiltonian systems of partial differential equations. Arch. Rational Mech. Anal. 5, 95–176 (1960).
Frölicher, A., & W. Bucher [1], Calculus in Vector Spaces without Norm. Berlin-Heidelberg-New York: Springer 1966.
Goldstein, H. [1], Classical Mechanics. Reading, Mass.: Addison Wesley 1950.
Gross, L. [1], The Cauchy problem for the coupled Maxwell and Dirac equations. Comm. on Pure and App. Math. 19, 1–15 (1966).
Hile, E., & R. Phillips [1], Functional Analysis and Semi-Groups. A.M.S. Providence R.I. (1967).
Hörmander, L. [1], Linear Differential Operators. Berlin-Göttingen-Heidelberg: Springer 1963.
Kato, T. [1], Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc. 70, 195–211 (1950).
Lang, S. [1], Introduction to Differentiable Manfolds. New York: Wiley 1966.
Lions, J. [1], Equations Différentielles Opérationelles. Berlin-Göttingen-Heidelberg: Springer 1961.
Marsden, J. [1], A Banach Space for Partial Differential Equations with Constant Coefficients (an unpublished note).
Marsden, J. [2], Generalized Hamiltonian mechanics. Arch. Rational Mech. Anal. 28, 323–361 (1968); Proceedings of the Symposium on Topological Dynamics. New York: Benjamin 1968.
Moser, J. [1], A new technique for the construction of solutions for non-linear differential equations. Proc. Nat. Acad. 47, 1824 (1961).
Moser, J. [2], A rapidly convergent iteration method and non-linear partial differential equations (I, II). Scuola Normale Superiore, Pisa XX (II) (1966) 265, 499.
Rohrlich, F. [1], Classical Charged Particles. Reading, Mass.: Addison-Wesley 1965.
Schweber, S.S. [1], An Introduction to Relativistic Quantum Field Theory. Evanston, Ill.: Row, Peterson & Co.
Segal, I.E. [1], Non-linear semi-groups. Ann. of Math. 78, 339–364 (1963).
Segal, I.E. [2], Mathematical Problems of Relativistic Physics. A.M.S., Providence, R.I. (1963).
Segal, I.E. [3], Differential operators in the manifold of solutions of a non-linear differential equation. Jour. de Math. XIIV, 72 (1965).
Sobolev, S. [1], Applications of Functional Analysis in Mathematical Physics. A.M.S. transl. (1963).
Truesdell, C., & W. Noll [1], The Non-linear Field Theories of Mechanics. Handbuch der Physik III/3. Berlin-Heidelberg-New York: Springer 1965.
Yosida, K. [1], Functional Analysis. Berlin-Heidelberg-New York: Springer 1965.
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Marsden, J.E. Hamiltonian one parameter groups a mathematical exposition of infinite dimensional Hamiltonian Systems with applications in classical and quantum mechanics. Arch. Rational Mech. Anal. 28, 362–396 (1968). https://doi.org/10.1007/BF00251662
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DOI: https://doi.org/10.1007/BF00251662