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Volumn 10, Issue 2, 2000, Pages 145-174

Hamiltonian oscillators in 1-1-1 resonance: Normalization and integrability

Author keywords

Integrability; Invariants; Normal forms; Oscillators; Reduction; Resonances; Symmetries

Indexed keywords


EID: 0005210494     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329910007     Document Type: Article
Times cited : (21)

References (48)
  • 2
    • 0039762400 scopus 로고
    • Periodic orbits in nearly axisymmetric stellar systems
    • Caranicolas, N. D., Barbanis, B.: Periodic Orbits in Nearly Axisymmetric Stellar Systems. Astronomy & Astrophysics 114 (1982) 360-366.
    • (1982) Astronomy & Astrophysics , vol.114 , pp. 360-366
    • Caranicolas, N.D.1    Barbanis, B.2
  • 3
    • 0040960041 scopus 로고
    • Resonant systems with three degrees of freedom
    • Contopoulos, G., Barbanis, B.: Resonant Systems with Three Degrees of Freedom. Astronomy & Astrophysics 153 (1985) 44-54.
    • (1985) Astronomy & Astrophysics , vol.153 , pp. 44-54
    • Contopoulos, G.1    Barbanis, B.2
  • 4
    • 0033099574 scopus 로고    scopus 로고
    • Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator
    • Cushman, R. H., Ferrer, S., Hanßmann, H.: Singular Reduction of Axially Symmetric Perturbations of the Isotropic Harmonic Oscillator. Nonlinearity 12 (1999) 389-410.
    • (1999) Nonlinearity , vol.12 , pp. 389-410
    • Cushman, R.H.1    Ferrer, S.2    Hanßmann, H.3
  • 5
    • 0007200238 scopus 로고
    • Hamiltonian chaos in nonlinear optical polarization dynamics
    • David, D., Holm, D. D., Tratnik, M. V.: Hamiltonian Chaos in Nonlinear Optical Polarization Dynamics. Physics Reports 187 (1990) 281-367.
    • (1990) Physics Reports , vol.187 , pp. 281-367
    • David, D.1    Holm, D.D.2    Tratnik, M.V.3
  • 8
    • 0007247629 scopus 로고
    • Stellar orbits in a triaxial galaxy. I. Orbits in the plane of rotation
    • de Zeeuw, T., Merritt, D.: Stellar Orbits in a Triaxial Galaxy. I. Orbits in the Plane of Rotation. The Astrophysical Journal 267 (1983) 571-595.
    • (1983) The Astrophysical Journal , vol.267 , pp. 571-595
    • De Zeeuw, T.1    Merritt, D.2
  • 9
    • 0000717287 scopus 로고
    • Canonical transformations depending on a small parameter
    • Deprit, A.: Canonical Transformations Depending on a Small Parameter. Celestial Mechanics 1 (1969) 12-30.
    • (1969) Celestial Mechanics , vol.1 , pp. 12-30
    • Deprit, A.1
  • 12
    • 0040365809 scopus 로고
    • Normalization of resonant hamiltonians
    • Ed. J. Seimenis, Plenum Press, New York
    • Farrelly, D., Humpherys, J., Uzer, T.: Normalization of Resonant Hamiltonians. In Hamiltonian Mechanics. Ed. J. Seimenis, Plenum Press, New York (1994) 237-244.
    • (1994) Hamiltonian Mechanics , pp. 237-244
    • Farrelly, D.1    Humpherys, J.2    Uzer, T.3
  • 13
    • 0001302205 scopus 로고    scopus 로고
    • On perturbed 3D elliptic oscillators: A case of critical inclination in galactic dynamics
    • New Trends for Hamiltonian Systems and Celestial Mechanics. Eds. E. A. Lacomba and J. Llibre, World Scientific, Singapore
    • Ferrer, S., Gárate, J.: On Perturbed 3D Elliptic Oscillators: A Case of Critical Inclination in Galactic Dynamics. In New Trends for Hamiltonian Systems and Celestial Mechanics. Eds. E. A. Lacomba and J. Llibre, Advanced Series in Nonlinear Dynamics 8, World Scientific, Singapore (1996) 179-197.
    • (1996) Advanced Series in Nonlinear Dynamics , vol.8 , pp. 179-197
    • Ferrer, S.1    Gárate, J.2
  • 14
    • 0000039278 scopus 로고    scopus 로고
    • On the hénon and heiles system in three dimensions: The role of the axial symmetry
    • Ferrer, S., Palacián, J., San Juan, J. F., Viartola, A., Yanguas, P.: On the Hénon and Heiles System in Three Dimensions: The Role of the Axial Symmetry. Physics Letters A 228 (1997) 255-260.
    • (1997) Physics Letters A , vol.228 , pp. 255-260
    • Ferrer, S.1    Palacián, J.2    San Juan, J.F.3    Viartola, A.4    Yanguas, P.5
  • 19
    • 0000576585 scopus 로고
    • 3 for all classical central potential problems
    • 3 for All Classical Central Potential Problems. Progress of Theoretical Physics 37 (1967) 798-812.
    • (1967) Progress of Theoretical Physics , vol.37 , pp. 798-812
    • Fradkin, D.M.1
  • 20
    • 0003225879 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer-Verlag, New York
    • Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences 42, Springer-Verlag, New York (1993).
    • (1993) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 21
    • 0003255969 scopus 로고
    • Chaos in classical and quantum mechanics
    • Springer-Verlag, New York
    • Gutzwiller, M. C.: Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics 1, Springer-Verlag, New York (1990).
    • (1990) Interdisciplinary Applied Mathematics , vol.1
    • Gutzwiller, M.C.1
  • 22
    • 0039968458 scopus 로고
    • Whiskered tori and chaos in resonant Hamiltonian normal forms
    • Haller, G., Wiggins, S.: Whiskered Tori and Chaos in Resonant Hamiltonian Normal Forms. Fields Institute Communications 4 (1995) 129-149.
    • (1995) Fields Institute Communications , vol.4 , pp. 129-149
    • Haller, G.1    Wiggins, S.2
  • 23
    • 0000318075 scopus 로고    scopus 로고
    • Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
    • Haller, G., Wiggins, S.: Geometry and Chaos near Resonant Equilibria of 3-DOF Hamiltonian Systems. Physica D 90 (1996) 319-365.
    • (1996) Physica D , vol.90 , pp. 319-365
    • Haller, G.1    Wiggins, S.2
  • 24
    • 0001230718 scopus 로고
    • A generalization of the runge-lenz constant of classical motion in a central potential
    • Holas, A., March, N. H.: A Generalization of the Runge-Lenz Constant of Classical Motion in a Central Potential. Journal of Physics A: Mathematical, Nuclear and General 23 (1990) 735-749.
    • (1990) Journal of Physics A: Mathematical, Nuclear and General , vol.23 , pp. 735-749
    • Holas, A.1    March, N.H.2
  • 26
    • 0002025569 scopus 로고
    • Chaos in the 1:2:3 Hamiltonian normal form
    • Hoveijn, I., Verhulst, F.: Chaos in the 1:2:3 Hamiltonian Normal Form. Physica D 44 (1990) 397-406.
    • (1990) Physica D , vol.44 , pp. 397-406
    • Hoveijn, I.1    Verhulst, F.2
  • 28
    • 0009325378 scopus 로고
    • On resonant hamiltonian systems with finitely many degrees of freedom
    • Local and Global Methods in Nonlinear Dynamics. Eds. A. V. Sáenz, W. W. Zachary and R. Cawley, Silver Spring
    • Kummer, M.: On Resonant Hamiltonian Systems with Finitely Many Degrees of Freedom. In Local and Global Methods in Nonlinear Dynamics. Eds. A. V. Sáenz, W. W. Zachary and R. Cawley, Lecture Notes in Physics 252, Silver Spring (1986) 19-31.
    • (1986) Lecture Notes in Physics , vol.252 , pp. 19-31
    • Kummer, M.1
  • 32
    • 0039773762 scopus 로고
    • The geometry of harmonic oscillators
    • Meyer, K. R.: The Geometry of Harmonic Oscillators. American Mathematical Monthly 97 (1990) 457-465.
    • (1990) American Mathematical Monthly , vol.97 , pp. 457-465
    • Meyer, K.R.1
  • 33
    • 0003221080 scopus 로고
    • Introduction to Hamiltonian dynamical systems and the N-body problem
    • Springer-Verlag, New York
    • Meyer, K. R., Hall, G. R.: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences 90, Springer-Verlag, New York (1992).
    • (1992) Applied Mathematical Sciences , vol.90
    • Meyer, K.R.1    Hall, G.R.2
  • 34
    • 84980148530 scopus 로고
    • Regularization of kepler's problem and the averaging method on a manifold
    • Moser, J.: Regularization of Kepler's Problem and the Averaging Method on a Manifold. Communications on Pure and Applied Mathematics 23 (1970) 609-636.
    • (1970) Communications on Pure and Applied Mathematics , vol.23 , pp. 609-636
    • Moser, J.1
  • 35
    • 84980140116 scopus 로고
    • Periodic orbits near an equilibrium and a theorem by alan weinstein
    • Moser, J.: Periodic Orbits Near an Equilibrium and a Theorem by Alan Weinstein. Communications on Pure and Applied Mathematics 29 (1976) 727-747.
    • (1976) Communications on Pure and Applied Mathematics , vol.29 , pp. 727-747
    • Moser, J.1
  • 36
    • 0001693467 scopus 로고
    • Dynamical symmetries and classical mechanics
    • Mukunda, N.: Dynamical Symmetries and Classical Mechanics. Physical Review: General Physics Series 155 (1967) 1383-1386.
    • (1967) Physical Review: General Physics Series , vol.155 , pp. 1383-1386
    • Mukunda, N.1
  • 37
    • 0003229603 scopus 로고
    • Averaging methods in nonlinear dynamical systems
    • Springer-Verlag, New York
    • Sanders, J. A., Verhulst, F.: Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences 59, Springer-Verlag, New York (1985).
    • (1985) Applied Mathematical Sciences , vol.59
    • Sanders, J.A.1    Verhulst, F.2
  • 40
    • 0039181350 scopus 로고
    • First-order resonances in three-degrees-of-freedom systems
    • van der Aa, E.: First-Order Resonances in Three-Degrees-of-Freedom Systems. Celestial Mechanics 31 (1983) 163-191.
    • (1983) Celestial Mechanics , vol.31 , pp. 163-191
    • Van Der Aa, E.1
  • 43
    • 0010675629 scopus 로고
    • The 1:2:2-resonance, its periodic orbits and integrals
    • Asymptotic Analysis. From Theory to Application. Ed. F. Verhulst, Springer-Verlag, Berlin
    • van der Aa, E., Sanders, J. A.: The 1:2:2-Resonance, Its Periodic Orbits and Integrals. In Asymptotic Analysis. From Theory to Application. Ed. F. Verhulst, Lecture Notes in Mathematics 711, Springer-Verlag, Berlin (1979) 187-208.
    • (1979) Lecture Notes in Mathematics , vol.711 , pp. 187-208
    • Van Der Aa, E.1    Sanders, J.A.2
  • 45
    • 0000384553 scopus 로고    scopus 로고
    • Symmetry and integrability in Hamiltonian normal forms
    • Eds. D. Bambusi and G. Gaeta, Quaderni GNFM, Firenze (to appear)
    • Verhulst, F.: Symmetry and Integrability in Hamiltonian Normal Forms. In Symmetry and Perturbation Theory. Eds. D. Bambusi and G. Gaeta, Quaderni GNFM, Firenze (to appear).
    • Symmetry and Perturbation Theory
    • Verhulst, F.1
  • 46
    • 0001459972 scopus 로고
    • Normal modes for nonlinear Hamiltonian systems
    • Weinstein, A.: Normal Modes for Nonlinear Hamiltonian Systems. Inventiones Mathematicae 20 (1973) 47-57.
    • (1973) Inventiones Mathematicae , vol.20 , pp. 47-57
    • Weinstein, A.1
  • 47
    • 0008652530 scopus 로고
    • Chaotic transport in dynamical systems
    • Springer-Verlag, New York
    • Wiggins, S.: Chaotic Transport in Dynamical Systems. Interdisciplinary Applied Mathematics 2, Springer-Verlag, New York (1992).
    • (1992) Interdisciplinary Applied Mathematics , vol.2
    • Wiggins, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.