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Journal articles on the topic 'Action-Angle variables'

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Published: 20 April 2024

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1

Spergel, David N. "Natural Action–Angle Variables." Symposium - International Astronomical Union 127 (1987): 483–84. http://dx.doi.org/10.1017/s0074180900185857.

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Since galaxies are collisionless relaxed systems, actions are an extremely useful tool for understanding their dynamics. There are many potential applications of actions: (1) When orbits in an N-body simulation are characterized by their actions, the six dimensional distribution function, can be reduced to a more tractable three dimensional function, f(J). (2) Actions are adiabatic invariants, and thus are useful for studying slowly evolving systems. Binney, May and Ostriker (1986) have applied this technique to study the response of the spheroid to the disc. (3) the spectral decomposition of an orbit can be used to help generate self–consistent galaxy models (Spergel 1987).

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2

Bates, Larry, and Jedrzej Śniatycki. "On action-angle variables." Archive for Rational Mechanics and Analysis 120, no. 4 (December 1992): 337–43. http://dx.doi.org/10.1007/bf00380319.

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3

YEON*, Kyu Hwang, and Eun Ji LIM. "Quantum Action-angle Variables." New Physics: Sae Mulli 63, no. 5 (May 31, 2013): 524–30. http://dx.doi.org/10.3938/npsm.63.524.

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4

Llave, R. de la, A. González, À. Jorba, and J. Villanueva. "KAM theory without action-angle variables." Nonlinearity 18, no. 2 (January 22, 2005): 855–95. http://dx.doi.org/10.1088/0951-7715/18/2/020.

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5

Lahiri, Abhijit, Gautam Ghosh, and T. K. Kar. "Action-angle variables in quantum mechanics." Physics Letters A 238, no. 4-5 (February 1998): 239–43. http://dx.doi.org/10.1016/s0375-9601(97)00926-2.

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6

Chavanis, Pierre-Henri. "Kinetic theory with angle–action variables." Physica A: Statistical Mechanics and its Applications 377, no. 2 (April 2007): 469–86. http://dx.doi.org/10.1016/j.physa.2006.11.078.

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7

Mahajan, S. M., and C. Y. Chen. "Plasma kinetic theory in action-angle variables." Physics of Fluids 28, no. 12 (1985): 3538. http://dx.doi.org/10.1063/1.865308.

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8

Bellucci, Stefano, Armen Nersessian, Armen Saghatelian, and Vahagn Yeghikyan. "Quantum Ring Models and Action-Angle Variables." Journal of Computational and Theoretical Nanoscience 8, no. 4 (April 1, 2011): 769–75. http://dx.doi.org/10.1166/jctn.2011.1751.

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9

Hakobyan, T., O. Lechtenfeld, A. Nersessian, A. Saghatelian, and V. Yeghikyan. "Action-angle variables and novel superintegrable systems." Physics of Particles and Nuclei 43, no. 5 (September 2012): 577–82. http://dx.doi.org/10.1134/s1063779612050152.

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10

Khein, Alexander, and D. F. Nelson. "Hannay angle study of the Foucault pendulum in action‐angle variables." American Journal of Physics 61, no. 2 (February 1993): 170–74. http://dx.doi.org/10.1119/1.17332.

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11

Lewis, H. Ralph, Walter E. Lawrence, and Joseph D. Harris. "Quantum Action-Angle Variables for the Harmonic Oscillator." Physical Review Letters 77, no. 26 (December 23, 1996): 5157–59. http://dx.doi.org/10.1103/physrevlett.77.5157.

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12

Campoamor-Stursberg, R., M. Gadella, Ş. Kuru, and J. Negro. "Action–angle variables, ladder operators and coherent states." Physics Letters A 376, no. 37 (July 2012): 2515–21. http://dx.doi.org/10.1016/j.physleta.2012.06.027.

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13

Hamilton, Mark D. "Classical and quantum monodromy via action–angle variables." Journal of Geometry and Physics 115 (May 2017): 37–44. http://dx.doi.org/10.1016/j.geomphys.2016.08.014.

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14

Reiman, A. H., and N. Pomphrey. "Computation of magnetic coordinates and action-angle variables." Journal of Computational Physics 94, no. 1 (May 1991): 225–49. http://dx.doi.org/10.1016/0021-9991(91)90144-a.

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15

Farrelly, David, and John A. Milligan. "Action-angle variables for the diamagnetic Kepler problem." Physical Review A 45, no. 11 (June 1, 1992): 8277–79. http://dx.doi.org/10.1103/physreva.45.8277.

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16

Ghosh, Aritra, and Chandrasekhar Bhamidipati. "Action-angle variables for the purely nonlinear oscillator." International Journal of Non-Linear Mechanics 116 (November 2019): 167–72. http://dx.doi.org/10.1016/j.ijnonlinmec.2019.06.012.

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17

Beals, Richard, and D. H. Sattinger. "Action-angle variables for the Gel'fand-Dikii flows." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 43, no. 2 (March 1992): 219–42. http://dx.doi.org/10.1007/bf00946628.

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18

Karimipour, V. "A solvable Hamiltonian system: Integrability and action-angle variables." Journal of Mathematical Physics 38, no. 3 (March 1997): 1577–82. http://dx.doi.org/10.1063/1.531907.

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19

Lechtenfeld, Olaf, Armen Nersessian, and Vahagn Yeghikyan. "Action-angle variables for dihedral systems on the circle." Physics Letters A 374, no. 46 (October 2010): 4647–52. http://dx.doi.org/10.1016/j.physleta.2010.09.047.

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20

Aharonov, Dov, and Uri Elias. "Parabolic fixed points, invariant curves and action-angle variables." Ergodic Theory and Dynamical Systems 10, no. 2 (June 1990): 231–45. http://dx.doi.org/10.1017/s0143385700005526.

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AbstractA fixed point of an area-preserving mapping of the plane is called elliptic if the eigenvalues of its linearization are of unit modulus but not ±1; it is parabolic if both eigenvalues are 1 or −1. The elliptic case is well understood by Moser's theory. Here we study when is a parabolic fixed point surrounded by closed invariant curves. We approximate our mapping T by the phase flow of an Hamiltonian system. A pair of variables, closely related to the action-angle variables, is used to reduce T into a twist mapping. The conditions for T to have closed invariant curves are stated in terms of the Hamiltonian.

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21

FUCHSSTEINER, BENNO, and GUDRUN OEVEL. "GEOMETRY AND ACTION-ANGLE VARIABLES OF MULTI SOLITON SYSTEMS." Reviews in Mathematical Physics 01, no. 04 (January 1989): 415–79. http://dx.doi.org/10.1142/s0129055x8900016x.

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For all completely integrable nonlinear hamiltonian systems which have a localized hereditary recursion operator, a complete action-angle variable representation is given for the multisoliton manifolds. Here multisoliton manifolds are defined as reductions with respect to suitable linear sums of symmetry generators. The embedding of these multisoliton manifolds, into the manifold of all solutions, is described in terms of the construction of its tangent bundle. The basis vectors of the respective tangent spaces are given by local densities. This local geometrical description of the tangent bundle turns out to be independent of the special structure of the particular equation under consideration. The principal tool for finding the necessary geometrical quantities are the canonical commutation relations for the so called mastersymmetries. These relations reflect the hereditary structure. All mastersymmetries turn out to be elements of the tangent space. Although the mastersymmetries, in the case under consideration, principally cannot be hamiltonian, suitable integrating factors are found which make them hamiltonian on the reduced manifold. So, up to suitable linear combinations, the mastersymmetries are shown to correspond to the angle variables. The action-angle-structure found in this way is put into one-to-one correspondence with the spectrum of the recursion operator. The spectrum of this operator is shown to be of multiplicity two and all its eigenvectors are explicitly constructed. Again, this construction is of a canonical nature, i.e., independent of the particular equation under consideration. For vanishing boundary conditions the given action-angle-structure is compared to the asymptotic data (speeds and phases), and the gradients of these global asymptotic data are given in terms of local quantities. It turns out that for all times during the evolution the derivatives of the field function with respect to any particular asymptotic datum yields an eigenvector of the recursion operator. Thus a method is given for reconstructing the spectral resolution of the recursion operator by partial derivatives. This method yields new methods of solution for other equations (for example the singularity equation and the Harry Dym equation). The superposition formula for phase shifts is shown to hold in all generality for the systems under consideration. Several examples are given. An extensive comparison of the present results with the work of others is carried out.

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22

Kulish, P. P. "Action-angle variables for a multicomponent nonlinear Schrödinger equation." Journal of Soviet Mathematics 28, no. 5 (March 1985): 705–13. http://dx.doi.org/10.1007/bf02112335.

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23

Jovanovic, Božidar. "Noncommutative integrability and action–angle variables in contact geometry." Journal of Symplectic Geometry 10, no. 4 (2012): 535–61. http://dx.doi.org/10.4310/jsg.2012.v10.n4.a3.

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24

Fernandes, Rui Loja, Camille Laurent-Gengoux, and Pol Vanhaecke. "Global action-angle variables for non-commutative integrable systems." Journal of Symplectic Geometry 16, no. 3 (2018): 645–99. http://dx.doi.org/10.4310/jsg.2018.v16.n3.a3.

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25

Teğmen, Adnan. "Momentum Map and Action-Angle Variables for Nambu Dynamics." Czechoslovak Journal of Physics 54, no. 7 (July 2004): 749–57. http://dx.doi.org/10.1023/b:cjop.0000038528.44335.8b.

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26

McKean, H. P., and K. L. Vaninsky. "Action-angle variables for the cubic Schr�dinger equation." Communications on Pure and Applied Mathematics 50, no. 6 (June 1997): 489–562. http://dx.doi.org/10.1002/(sici)1097-0312(199706)50:6<489::aid-cpa1>3.0.co;2-4.

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27

Bates, Larry M. "Examples for obstructions to action-angle coordinates." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 110, no. 1-2 (1988): 27–30. http://dx.doi.org/10.1017/s0308210500024823.

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SynopsisWe give examples of symplectic manifolds which are also non-trivial principal torus-bundles with Lagrangian fibres. These bundles are examples of spaces with an obstruction to the global existence of action-angle variables.

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28

Kantonistova, E. O. "Integer lattices of action-angle variables for “spherical pendulum” system." Moscow University Mathematics Bulletin 69, no. 4 (July 2014): 135–47. http://dx.doi.org/10.3103/s0027132214040019.

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29

Lara, Martin, and Sebastián Ferrer. "Expanding the simple pendulum's rotation solution in action-angle variables." European Journal of Physics 36, no. 5 (August 6, 2015): 055040. http://dx.doi.org/10.1088/0143-0807/36/5/055040.

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30

Binney, James. "Angle-action variables for orbits trapped at a Lindblad resonance." Monthly Notices of the Royal Astronomical Society 495, no. 1 (May 19, 2020): 886–94. http://dx.doi.org/10.1093/mnras/staa092.

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ABSTRACT The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasi-periodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.

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31

OH, PHILLIAL, and MYUNG-HO KIM. "ACTION ANGLE VARIABLES FOR COMPLEX PROJECTIVE SPACE AND SEMICLASSICAL EXACTNESS." Modern Physics Letters A 09, no. 36 (November 30, 1994): 3339–46. http://dx.doi.org/10.1142/s0217732394003166.

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We construct the action angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Schrödinger equation.

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32

Hirota, M., and Y. Fukumoto. "Action-angle variables for the continuous spectrum of ideal magnetohydrodynamics." Physics of Plasmas 15, no. 12 (December 2008): 122101. http://dx.doi.org/10.1063/1.3035912.

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33

Davis, Edward D., and Ghassan I. Ghandour. "On the use of angle-action variables in semiclassical mechanics." Physics Letters A 309, no. 1-2 (March 2003): 1–4. http://dx.doi.org/10.1016/s0375-9601(03)00174-9.

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34

BELLUCCI, STEFANO, ARMEN NERSESSIAN, and VAHAGN YEGHIKYAN. "ACTION-ANGLE VARIABLES FOR THE PARTICLE NEAR EXTREME KERR THROAT." Modern Physics Letters A 27, no. 32 (October 11, 2012): 1250191. http://dx.doi.org/10.1142/s021773231250191x.

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We construct the action-angle variables for the spherical part of conformal mechanics describing the motion of a particle near extreme Kerr throat. We indicate the existence of the critical point |pφ| = mc R Sch (with m being the mass of the particle, c denoting the speed of light, [Formula: see text] being the Schwarzschild radius of a black hole with mass M, and γ denoting the gravitational constant), where these variables are expressed in elementary functions. Out from this point the action-angle variables are defined by the elliptic integrals. The proposed formulation allows one to easily reconstruct the whole dynamics of the particle both in initial coordinates, as well as in the so-called conformal basis, where the Hamiltonian takes the form of conventional non-relativistic conformal mechanics. The related issues, such as semiclassical quantization and supersymmetrization are also discussed.

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35

Postell, V., and T. Uzer. "Quantization of the asymmetric top using quantum action-angle variables." Physical Review A 41, no. 7 (April 1, 1990): 4035–37. http://dx.doi.org/10.1103/physreva.41.4035.

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36

Smith, T. B., and John A. Vaccaro. "Comment on “Quantum Action-Angle Variables for the Harmonic Oscillator”." Physical Review Letters 80, no. 12 (March 23, 1998): 2745. http://dx.doi.org/10.1103/physrevlett.80.2745.

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37

Zung, Nguyen Tien. "A Conceptual Approach to the Problem of Action-Angle Variables." Archive for Rational Mechanics and Analysis 229, no. 2 (February 27, 2018): 789–833. http://dx.doi.org/10.1007/s00205-018-1227-3.

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38

Tolkachev, V. A. "Semiclassical asymmetric top in action–angle variables with binary stereodynamics." Journal of Applied Spectroscopy 79, no. 6 (January 2013): 962–68. http://dx.doi.org/10.1007/s10812-013-9700-0.

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39

Wiesel, William E. "Canonical Floquet Theory II: Action-Angle Variables Near Conservative Periodic Orbits." Journal of the Astronautical Sciences 68, no. 2 (March 25, 2021): 391–401. http://dx.doi.org/10.1007/s40295-021-00258-z.

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40

Bibik, Yu V. "Action-angle variables for an extension of the Lotka-Volterra system." Applied Mathematical Sciences 7 (2013): 665–77. http://dx.doi.org/10.12988/ams.2013.13060.

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41

Luis, A., and L. L. Sánchez-Soto. "Canonical transformations to action and phase-angle variables and phase operators." Physical Review A 48, no. 1 (July 1, 1993): 752–57. http://dx.doi.org/10.1103/physreva.48.752.

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42

Hakobyan, T., O. Lechtenfeld, A. Nersessian, A. Saghatelian, and V. Yeghikyan. "Integrable generalizations of oscillator and Coulomb systems via action–angle variables." Physics Letters A 376, no. 5 (January 2012): 679–86. http://dx.doi.org/10.1016/j.physleta.2011.12.034.

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43

Kiesenhofer, Anna, Eva Miranda, and Geoffrey Scott. "Action-angle variables and a KAM theorem for b-Poisson manifolds." Journal de Mathématiques Pures et Appliquées 105, no. 1 (January 2016): 66–85. http://dx.doi.org/10.1016/j.matpur.2015.09.006.

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44

Kappeler, T., and M. Makarov. "On Action-Angle Variables¶for the Second Poisson Bracket of KdV." Communications in Mathematical Physics 214, no. 3 (November 2000): 651–77. http://dx.doi.org/10.1007/s002200000282.

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45

González-Martínez, M. L., L. Bonnet, P. Larrégaray, J. C. Rayez, and J. Rubayo-Soneira. "Transformation from angle-action variables to Cartesian coordinates for polyatomic reactions." Journal of Chemical Physics 130, no. 11 (March 21, 2009): 114103. http://dx.doi.org/10.1063/1.3089602.

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46

Constantin, Adrian, and Rossen Ivanov. "Poisson Structure and Action-Angle Variables for the Camassa–Holm Equation." Letters in Mathematical Physics 76, no. 1 (March 1, 2006): 93–108. http://dx.doi.org/10.1007/s11005-006-0063-9.

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47

McKean, H. P., and K. L. Vaninsky. "Cubic Schr�dinger: The petit canonical ensemble in action-angle variables." Communications on Pure and Applied Mathematics 50, no. 7 (July 1997): 593–622. http://dx.doi.org/10.1002/(sici)1097-0312(199707)50:7<593::aid-cpa1>3.0.co;2-2.

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48

Bogdanov, E. I. "Action-angle variables in the theory of superconductivity and superfluidity phenomena." Russian Physics Journal 40, no. 5 (May 1997): 465–74. http://dx.doi.org/10.1007/bf02508777.

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49

Kretzschmar, Martin. "A Theory of Anharmonic Perturbations in a Penning Trap." Zeitschrift für Naturforschung A 45, no. 8 (August 1, 1990): 965–78. http://dx.doi.org/10.1515/zna-1990-0805.

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AbstractClassical hamiltonian perturbation theory formulated in terms of action-angle variables is applied to develop a general and systematic method for calculating the influence of anharmonic perturbations on the motion of a charged particle in a Penning trap. Action-angle variables are ideally suited to determine the shifts of the characteristic frequencies in a perturbed orbit. The application of the method is demonstrated by several case studies

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50

Visinescu, Mihai. "Complete integrability of geodesics in Sasaki-Einstein spaceYp,qvia action-angle variables." Journal of Physics: Conference Series 845 (May 2017): 012021. http://dx.doi.org/10.1088/1742-6596/845/1/012021.

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