This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
M. Andoyer, (1923), Cours de Mécanique Céleste, Vol I, Gauthier-Villars, Paris.AndoyerM.1923IGauthier-VillarsParisSearch in Google Scholar
H. Broer et al., (2003), Bifurcations in Hamiltonian Systems. Computing Singularities by Gröner Bases, Springer-Verlag, Berlin-Heidelberg. 10.1007/b10414BroerH.2003Springer-VerlagBerlin-Heidelberg10.1007/b10414Open DOISearch in Google Scholar
T. Becker and V. Weispfenning, (1993), Gröner bases. A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics, Springer-Verlag, New York. 10.1007/978-1-4612-0913-3BeckerT.WeispfenningV.1993Graduate Texts in Mathematics, Springer-VerlagNew York10.1007/978-1-4612-0913-3Open DOISearch in Google Scholar
D.A. Cox, J. Little and D. O’Shea, (2007), Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, Springer-Verlag, New York. 10.1007/978-0-387-35651-8CoxD.A.LittleJ.O’SheaD.2007Undergraduate Texts in Mathematics, Springer-VerlagNew York10.1007/978-0-387-35651-8Open DOISearch in Google Scholar
F. Crespo, (2015), Hopf Fibration Reduction of a Quartic Model. An Application to Rotational and Orbital Dynamics, Ph.D. thesis, Universidad de Murcia, 2015, 208 pp.CrespoF.2015Universidad de Murcia2015208Search in Google Scholar
R.H. Cushman, (1984), Normal form for Hamiltonian vectorfields with periodic flow, S. Sternberg (Ed.), Differential Geometric Methods in Mathematical Physics, D. Reidel, Dordrecht (1984), pp. 125-144CushmanR.H.1984SternbergS.Differential Geometric Methods in Mathematical PhysicsReidelD.Dordrecht1984125144Search in Google Scholar
K. Efstathiou and D. Sadovskií, (2005), No polar coordinates (R.H. Cushman), in J. Montaldi and T. Ratiu (eds.) Geometric Mechanics and Symmetry: The Peyresq Lectures. Cambridge: Cambridge University Press, pp. 211-302. 10.1017/CBO9780511526367.005EfstathiouK.SadovskiíD.2005MontaldiJ.RatiuT.Geometric Mechanics and Symmetry: The Peyresq Lectures. Cambridge: Cambridge University Press21130210.1017/CBO9780511526367.005Open DOISearch in Google Scholar
R.H. Cushman and L. Bates, (1997), Global Aspects of Classical Integrable Systems, Birkhäuser Verlag, Basel. 10.1007/978-3-0348-8891-2CushmanR.H.BatesL.1997Birkhäuser VerlagBasel10.1007/978-3-0348-8891-2Open DOISearch in Google Scholar
R. Cushman, S. Ferrer and H. Hanßmann, (1999), Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator, Nonlinearity, 12, 389-410. 10.1088/0951-7715/12/2/014CushmanR.FerrerS.HanßmannH.1999Nonlinearity1238941010.1088/0951-7715/12/2/014Open DOISearch in Google Scholar
R.H. Cushman and D.A. Sadovskií, (2000), Monodromy in the hydrogen atom in crossed fields, Physica D: Nonlinear Phenomena, 142, No 1-2, 166-196. 10.1016/S0167-2789(00)00053-1CushmanR.H.SadovskiíD.A.2000Monodromy in the hydrogen atom in crossed fields1421-216619610.1016/S0167-2789(00)00053-1Open DOISearch in Google Scholar
A. Deprit, (1967), Free Rotation of a Rigid Body Studied in the Phase Plane, American Journal of Physics, 35, 424-428. 10.1119/1.1974113DepritA.1967American Journal of Physics3542442810.1119/1.1974113Open DOISearch in Google Scholar
A. Deprit, (1969), Canonical transformations depending on a small parameter, Celestial mechanics, 1, No 1, 12-30. 10.1007/BF01230629DepritA.1969Canonical transformations depending on a small parameter11123010.1007/BF01230629Open DOISearch in Google Scholar
A. Deprit, (1981), The elimination of the parallax in satellite theory, Celestial mechanics, 24, No 2, 111-153. 10.1007/BF01229192DepritA.1981The elimination of the parallax in satellite theory24211115310.1007/BF01229192Open DOISearch in Google Scholar
A. Deprit, (1982), Delaunay normalizations, Celestial mechanics, 26, No 1, 9-21. 10.1007/BF01233178DepritA.1982Delaunay normalizations26192110.1007/BF01233178Open DOISearch in Google Scholar
A. Elipe and A. Deprit, (1999), Oscillators in resonance, Mechanics Research Communications, 26, No 6, 635-640. 10.1016/S0093-6413(99)00072-5ElipeA.DepritA.1999Oscillators in resonance26663564010.1016/S0093-6413(99)00072-5Open DOISearch in Google Scholar
A. Deprit, (1991), The Lissajous transformation I. Basics, Celestial mechanics, 51, No 3, 201-225. 10.1007/BF00051691DepritA.1991The Lissajous transformation I. Basics51320122510.1007/BF00051691Open DOISearch in Google Scholar
G. Díaz et al., (2009), Generalized Van der Waals 4−D oscillator. Invariant tori and relative equilibria inξ = l = 0 surface, in: Actas de las XI Jornadas de Mecánica Celeste (Ezcaray, Spain, June 25-27, 2008) / Ed. V. Lanchares, A. Elipe. - Zaragoza : Real Academia de Ciencias de Zaragoza, 2009. - (Monografías de la Real Academia de Ciencias de Zaragoza ; 32). - p. 19-37DíazG.20091937Search in Google Scholar
G. Díaz et al., (2010), Relative equilibria and bifurcations in the generalized van der Waals 4D oscillator, Physica D: Nonlinear Phenomena, 239, No 16, 1610-1625. 10.1016/j.physd.2010.04.012DíazG.2010Relative equilibria and bifurcations in the generalized van der Waals 4D oscillator239161610162510.1016/j.physd.2010.04.012Open DOISearch in Google Scholar
K. Efstathiou, R.H. Cushman and D.A. Sadovskií, (2004), Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields, Physica D: Nonlinear Phenomena, 194, No 3-4, 250-274. 10.1016/j.physd.2004.03.003EfstathiouK.CushmanR.H.SadovskiíD.A.2004Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields1943-425027410.1016/j.physd.2004.03.003Open DOISearch in Google Scholar
J. Egea, (2007), Sistemas Hamiltonianos en resonancia 1:1:1:1. Reducciones toroidales y Bifurcaciones de Hopf, Tesis Doctoral, Universidad de Murcia, 180 pp.EgeaJ.2007Tesis Doctoral, Universidad de Murcia180Search in Google Scholar
J. Egea, S. Ferrer and J. V. der Meer, (2007), Hamiltonian fourfold 1:1 resonance with two rotational symmetries, Regular and Chaotic Dynamics, 12, No 6, 664-674. 10.1134/S1560354707060081EgeaJ.FerrerS.der MeerJ. V.2007Hamiltonian fourfold 1:1 resonance with two rotational symmetries12666467410.1134/S1560354707060081Open DOISearch in Google Scholar
A. Elipe and S. Ferrer, (1994), Reductions, relative equilibria, and bifurcations in the generalized van der Waals potential: Relation to the integrable cases, Physical Review Letters, 72, 985-988. 10.1103/PhysRevLett.72.985ElipeA.FerrerS.1994Reductions, relative equilibria, and bifurcations in the generalized van der Waals potential: Relation to the integrable cases7298598810.1103/PhysRevLett.72.98510056588Open DOISearch in Google Scholar
F. Fassò, (2005), Superintegrable Hamiltonian Systems: Geometry and Perturbations, Acta Applicandae Mathematica, 87, No 1, 93-121. 10.1007/s10440-005-1139-8FassòF.2005Superintegrable Hamiltonian Systems: Geometry and Perturbations8719312110.1007/s10440-005-1139-8Open DOISearch in Google Scholar
S. Ferrer, (2010), The Projective Andoyer transformation and the connection between the 4−D isotropic oscillator and Kepler systems, arXiv:1011.3000v1 [nlin.SI]. 1011.3000v1FerrerS.2010arXiv:1011.3000v1 [nlin.SI]1011.3000v1Open DOISearch in Google Scholar
S. Ferrer, J. Palacián and P. Yanguas, (2000), Hamiltonian Oscillators in 1-1-1 Resonance: Normalization and Integrability, Journal of Nonlinear Science, 10, No 2, 145-174. 10.1007/s003329910007FerrerS.PalaciánJ.YanguasP.2000Hamiltonian Oscillators in 1-1-1 Resonance: Normalization and Integrability10214517410.1007/s003329910007Open DOISearch in Google Scholar
S. Ferrer et al., (2002), On perturbed oscillators in 1-1-1 resonance: the case of axially symmetric cubic potentials, Journal of Geometry and Physics, 40, No 3-4, 320-369. 10.1016/S0393-0440(01)00041-9FerrerS.2002On perturbed oscillators in 1-1-1 resonance: the case of axially symmetric cubic potentials403-432036910.1016/S0393-0440(01)00041-9Open DOISearch in Google Scholar
S. Ferrer and F. Crespo, (2014), Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems, The Journal of Geometric Mechanics, 6, No 4, 479-502. 10.3934/jgm.2014.6.479FerrerS.CrespoF.2014Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems6447950210.3934/jgm.2014.6.479Open DOISearch in Google Scholar
S. Ferrer and M. Lara, (2010), Families of canonical transformations by Hamilton-Jacobi-Poincaré’ equation. Application to rotational and orbital motion, The Journal of Geometric Mechanics, 2, No 3, 223-241. 10.3934/jgm.2010.2.223FerrerS.LaraM.2010Families of canonical transformations by Hamilton-Jacobi-Poincaré’ equation. Application to rotational and orbital motion2322324110.3934/jgm.2010.2.223Open DOISearch in Google Scholar
M. Iñarrea et al., (2004), The Keplerian regime of charged particles in planetary magnetospheres, Physica D: Nonlinear Phenomena, 197, No 3-4, 242-268. 10.1016/j.physd.2004.07.009IñarreaM.2004The Keplerian regime of charged particles in planetary magnetospheres1973-424226810.1016/j.physd.2004.07.009Open DOISearch in Google Scholar
P. Kustaanheimo and E.L. Stiefel, (1965), Perturbation theory of Kepler motion based on spinor regularization, Journal für die reine und angewandte Mathematik (Crelles Journal), 218, 204-219. 10.1515/crll.1965.218.204KustaanheimoP.StiefelE.L.1965Perturbation theory of Kepler motion based on spinor regularization21820421910.1515/crll.1965.218.204Open DOISearch in Google Scholar
S. Mayer, J. Scheurle and S. Walcher, (2004), Practical normal form computations for vector fields, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 84, No 7, 472-482. 10.1002/zamm.200310115MayerS.ScheurleJ.WalcherS.2004Practical normal form computations for vector fields84747248210.1002/zamm.200310115Open DOISearch in Google Scholar
K. R. Meyer, G. R. Hall and D. Offin, (2009), Introduction to Hamiltonian Dynamical Systems and the N−Body Problem, Springer-Verlag, New York. 10.1007/978-0-387-09724-4MeyerK. R.HallG. R.OffinD.2009Springer-VerlagNew York10.1007/978-0-387-09724-4Open DOISearch in Google Scholar
J. Moser and E. J. Zehnder, (2005), Notes on Dynamical Systems, Courant Lecture Notes Vol. 12, AMS and the Courant Institute of Mathematical Sciences at New York University.MoserJ.ZehnderE. J.2005Notes on Dynamical Systems10.1090/cln/012Search in Google Scholar
N. N. Nehorošev, (1972), Action-angle variables, and their generalizations, Tr. Mosk. Mat. Obs., 26, MSU, M., 181-198.NehoroševN. N.1972Action-angle variables, and their generalizations181198Search in Google Scholar
G. Reeb, (1952), Sur certaines propriétés topologiques des variétés feuilletées, Acad. Roy. Belgique. Cl. Sci. Mém. Coll. in 8, 27.ReebG.1952Sur certaines propriétés topologiques des variétés feuilletées827Search in Google Scholar
J.A. Sanders, F. Verhulst and J. Murdock, (2007), Averaging Methods in Nonlinear Dynamical Systems, Vol. 59, Springer New York, New York. 10.1007/978-0-387-48918-6SandersJ.A.VerhulstF.MurdockJ.200759Springer New YorkNew York10.1007/978-0-387-48918-6Open DOISearch in Google Scholar
P. Yanguas et al., (2008), Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem, SIAM Journal on Applied Dynamical Systems 7, No 2, 311-340. 10.1137/070696453YanguasP.2008Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem7231134010.1137/070696453Open DOISearch in Google Scholar
J.C. van der Meer, (2015), The Kepler system as a reduced 4D harmonic oscillator, Journal of Geometry and Physics, 92, 181-193. 10.1016/j.geomphys.2015.02.016van der MeerJ.C.2015The Kepler system as a reduced 4D harmonic oscillator9218119310.1016/j.geomphys.2015.02.016Open DOISearch in Google Scholar