Bibliography
Abraham, R., & J. Marsden [1], Foundations of Mechanics. New York: Benjamin 1967.
Apostol, T. [1], Mathematical Analysis. Reading, Mass.: Addison Wesley 1957.
Arnold, V., & A. Avez [1], Problèmes ergodiques de la mechanique classique. Paris: Gauthier-Villars 1967.
Beltrami, E. [1], Pointwise and norm convergence of distributions. Jour. Math. Mech. 14, 99–107 (1965).
Beltrami, E. [2], Some alternative approaches to distributions. SIAM Rev. 5, 351–357 (1963).
Berberian, S. [1], Measure and Integration. New York: MacMillan 1965.
Billingsly, P. [1], Ergodic Theory and Information. New York: Wiley 1965.
Bouix, M. [1], Les fonctions généralisées ou distributions. Paris: Masson 1964.
Eells, J. [1], Geometric aspects of currents and distributions. Proc. Nat. Acad. of Sci. 41, 493–496 (1955).
Ehrenpreis, L. [1], Theory of Distributions for Locally Compact Spaces. Memoirs of A.M.S., Providence, R. I. (1956).
Garsoux, J. [1], Espaces vectoriels topologiques et distributions. Paris: Dunod 1963.
Gelfand, I. [1–4], Generalized Functions, Vols. I–IV. New York: Academic Press 1962.
Halperin, I. [1], Introduction to the Theory of Distributions. Univ. of Toronto Press (1952).
Halmos, P. [1], Measure Theory. Princeton: Van Nostrand 1950.
Halmos, P. [2], (&) J. vonNeumann, Operator methods in classical mechanics. Ann. of Math. 43, 332–350 (1942).
Halmos, P. [3], Lectures on Ergodic Theory. New York: Chelsea 1956.
Helgason, S. [1], Differential Geometry and Symmetric Spaces. New York: Academic Press 1962.
Jones, D. [1], Generalized Functions. London: McGraw-Hill 1966.
Kelley, J. [1], General Topology. Princeton: Van Nostrand 1955.
Koopman, B. [1], Hamiltonian systems and transformations in Hilbert space. Proc. Nat. Acad. Sci. 17, 315–318 (1931).
Marsden, J. [1], Hamiltonian one parameter groups. Arch. Rational Mech. Anal. 28, 362–396 (1968).
Marsden, J. [2], A correspondence principle for momentum operators. Can. Math. Bull. 10, 247–250 (1967).
Marsden, J. [3] Distributions on Manifolds (mimeographed). Princeton University (1966).
Marsden, J. [4], (& A.S. Wightman), Lectures on Statistical Mechanics (mimeographed). Princeton University (1967).
Marsden, J. [5], Non-smooth geodesic flows and classical mechanics (Can. Math. Bull., to appear).
Milnor, J. [1], Morse Theory. Ann of Math. Studies, Princeton (1961).
Nachbin, L. [1], Lectures on the Theory of Distributions. Instituto de Fisica E Mathemática, Universidade do Recife (1964).
Neumann, J. Von [1], Zur Operatorenmethode in der klassischen Mechanik. Ann. of Math. 33, 587, 789 (1932).
Rham, G. De [l], Variétés Différentiables. Paris: Hermann 1960.
Riss, J. [1], Eléments de calcul différentiel et théorie des distributions sur les groupes abéliens localement compacts. Acta. Math. 89, 45–105 (1953).
Schwartz, L. [1–2], Theorie des distributions (I, II). Paris: Hermann 1950.
Schwartz, L. [3], Théorie des distributions. Paris: Hermann 1966.
Segal, I. [1], Quantization of non-linear systems. Jour. Math. Phys. 1, 468–488 (1960).
Smale, S. [1], Differentiable dynamical systems. Am. Math. Soc. Bull. (to appear).
Spivac, M. [1], Calculus on Manifolds. New York: Benjamin 1965.
Sobolev, S.L. [1], Applications of functional analysis in mathematical physics. Transl. of Am. Math. Soc. 7 (1963).
Sternberg, S. [1], Lectures on Differential Geometry. Englewood Cliffs, N.J.: Prentice Hall 1964.
Temple, G. [1], The theory of generalized functions. Proc. Royal Soc. A 228, 1750–190 (1955).
Tondeur, P. [1], Lie Groups and Transformation Groups. Berlin-Heidelberg-New York: Springer 1966.
Yosida, K. [1], Functional Analysis. Berlin-Heidelberg-New York: Springer 1965.
Zemanian, A. [1], Distribution Theory and Transform Analysis. New York: McGraw-Hill 1965.
Author information
Authors and Affiliations
Additional information
Communicated by C. Truesdell
Rights and permissions
About this article
Cite this article
Marsden, J.E. Generalized Hamiltonian mechanics a mathematical exposition of non-smooth dynamical systems and classical Hamiltonian mechanics. Arch. Rational Mech. Anal. 28, 323–361 (1968). https://doi.org/10.1007/BF00251661
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00251661