×

zbMATH — the first resource for mathematics

Bifurcations and Hamilton’s principle. (English) Zbl 0366.58003

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57R70 Critical points and critical submanifolds in differential topology
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] AB-R Abraham, R., Robbin, J.: Transversal Mappings and Flows. New York: Beniamin, 1967 · Zbl 0171.44404
[2] AR Arnold, V.I.: Mathematical Methods of Classical Mechanics. (In Russian). Moscow: Nauk (1974) (English translation by K. Vogtmann and A. Weinstein. Graduate Texts in Mathematics, vol. 60. Berlin-Heidelberg-New York: springer 1978)
[3] B Bott, R.: Non-degenerate critical manifolds. Ann. of Math., II. Ser.60, 248-261 (1954) · Zbl 0058.09101 · doi:10.2307/1969631
[4] BK Bottkol, M.: Bifurcation of periodic orbits on manifolds, and Hamiltonian systems. Bull. Amer. Math. Soc.83, 1060-1062 (1977) · Zbl 0369.58014 · doi:10.1090/S0002-9904-1977-14384-X
[5] C-M Chernoff, P., Marsden, J.: Properties of Infinite Dimensional Hamiltonian Systems. Lecture Notes in Mathematics425. Berlin-Heidelberg-New York: Springer 1974
[6] F Fuller, F.B.: An index of fixed point type for periodic orbits. Amer. J. Math.89, 133-148 (1967) · Zbl 0152.40204 · doi:10.2307/2373103
[7] G Goldstein, H.: Classical Mechanics. Reading, MA: Addison-Wesley 1959 · Zbl 0043.18001
[8] K Klingenberg, W.: Closed Geodesics. Grundlehren der Mathematischen Wissenschaften vol.230. Berlin-Heidelberg-New York: Springer 1978 · Zbl 0397.58018
[9] ME Meyer, W.: Kritische Mannigfaltigkeiten in Hilbertmannigfaltigkeiten. Math. Ann.170, 45-66 (1967) · Zbl 0142.21604 · doi:10.1007/BF01362286
[10] MO Moser, J.: Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Commun. pure appl. Math29, 727-747 (1976) · Zbl 0346.34024 · doi:10.1002/cpa.3160290613
[11] P Palais, R.: Foundations of Global Non-linear Analysis. New York: Benjamin 1968. · Zbl 0164.11102
[12] R Reeken, M.: Stability of critical points under small perturbations. Part II: Analytic theory. Manuscripta math.8, 69-92 (1973) · Zbl 0248.58004 · doi:10.1007/BF01317578
[13] SM Smale, S.: Topology and mechanics, I, II. Inventiones math.10305-331 (1970);11, 45-64 (1970) · Zbl 0202.23201 · doi:10.1007/BF01418778
[14] SO Souriau, J.-M.: Structure des Systèmes Dynamiques. Paris: Dunod 1970 · Zbl 0186.58001
[15] W1 Weinstein, A.: Normal modes for nonlinear hamiltonian systems. Inventiones math.20, 47-57 (1973) · Zbl 0264.70020 · doi:10.1007/BF01405263
[16] W2 Weinstein, A.: Symplectic V-manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds. Commun. pure appl. Math.30, 265-271 (1977) · Zbl 0339.58007 · doi:10.1002/cpa.3160300207
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.