Frontiers and symmetries of dynamical systems
| dc.contributor.author | Díaz-Cano Ocaña, Antonio | |
| dc.contributor.author | Gonzalez Gascón, F. | |
| dc.date.accessioned | 2023-06-20T00:10:42Z | |
| dc.date.available | 2023-06-20T00:10:42Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | The frontiers of boundedness F(b) of the orbits of dynamical systems X defined on R(n) are studied. When X is completely integrable some topological properties of F(b) are found and, in certain cases, F(b) is localized with the help of symmetries of X. Several examples in dimensions 2 and 3 are provided. In case the number of known first integrals of the vector field X is less than n - 1, an interesting connection of F(b) with the frontier of boundedness of the level-sets of the first integrals of X is proved. This result also applies to Hamiltonian systems. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | GAAR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14984 | |
| dc.identifier.doi | 10.1080/14689361003761959 | |
| dc.identifier.issn | 1468-9367 | |
| dc.identifier.officialurl | http://www.tandfonline.com/doi/pdf/10.1080/14689361003761959 | |
| dc.identifier.relatedurl | http://www.tandfonline.com/loi/cdss20 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42136 | |
| dc.issue.number | 4 | |
| dc.journal.title | Dynamical Systems: An International Journal | |
| dc.language.iso | eng | |
| dc.page.final | 518 | |
| dc.page.initial | 501 | |
| dc.publisher | Taylor & Francis | |
| dc.relation.projectID | MTM2008-00272 | |
| dc.relation.projectID | Grupos UCM 910444. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Dynamical systems | |
| dc.subject.keyword | Frontier | |
| dc.subject.keyword | First integral | |
| dc.subject.keyword | Symmetries | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Frontiers and symmetries of dynamical systems | |
| dc.type | journal article | |
| dc.volume.number | 25 | |
| dcterms.references | L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Mechanics, Vol. 1, Pergamon Press, Oxford, New York, Toronto, Ontario, 1976. A. Díaz-Cano, F. Gonza´ lez-Gasco´ n, and D. Peralta-Salas, On scattering trajectories of dynamical systems, J. Math. Phys. 47 (2006), pp. 062703-1–062703-10. F. Dumortier, Singularities of vector fields on the plane, J. Diff. Eqns. 23 (1977), pp. 53–106. L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, Vol. 7, Springer-Verlag, New York, 1991. A. Bruno, Local Methods in Non-linear Differential Equations, Springer-Verlag, New York, 1989. H. Goldstein, Classical Mechanics, Addison-Wesley Series in Physics, Addison-Wesley, Cambridge, MA, 1980. C. Ehresmann, Sur la the´orie des variétés feuilletées, Univ. Roma. Ist. Naz. Alta Mat. Rend. Mat. Appl. 10 (1951), pp. 64–82. A. Kosinski, Differential Manifolds, Pure and Applied Mathematics, Vol. 138, Academic Press, Boston, 1993. J. Sivardie` re, A simple mechanical model exhibiting a spontaneous symmetry breaking, Amer. J. Phys. 51 (1983), pp. 1016–1018. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York, 1987. L. Tisza, On the general theory of phase transitions, in Phase Transitions in Solids (Symposium at Cornell University, August, 1948), R. Smoluchowski, J.E. Mayer, and W.A. Wevl, eds., Wiley, New York, 1951, pp. 1–37. G. Fletcher, A mechanical analog of first- and second-order phase transitions, Amer. J. Phys. 65 (1997), pp. 74–81. M. Berger and B. Gostiaux, Differential Geometry: Manifolds, Curves, and Surfaces, Springer, New York, 1988. A.F. Costa, F. González-Gascón, and A. González-López, On codimension one submersions of euclidean spaces, Invent. Math. 93 (1988), pp. 545–555. A. Borel and J.P. Serre, Impossibilité de fibrer un espace euclidien par des fibres compactes, C. R. Acad. Sci. Paris 230 (1950), pp. 2258–2260. Z. Jelonek, Geometry of real polynomial mappings, Math. Z. 239 (2002), pp. 321–333. H.O. Peitgen and P.H. Richter, The Beauty of Fractals: Images of Complex Dynamical Systems, Springer, New York, 1986. S. Nikiel and A. Goinski, Generation of volumetric escape time fractals, Comput. Grafics 27 (2003), pp. 977–982. P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986. R. Hermann, Differential Geometry and the Calculus of Variations, Math. Sci. Press, Massachusetts, 1977. J. Jackson, Classical Electrodynamics, John Wiley & Sons, Inc., New York, London, Sydney, 1975. L. Markus, Parallel dynamical systems, Topology 8 (1969), pp. 47–57. V. Nemytskii and V. Stepanov, Theory of Differential Equations, Princeton University Press, Princeton, 1960. F. Gonza´ lez-Gasco´ n and A. Gonza´ lez-Lo´ pez, Another method for the obtention of first integrals of dynamical systems, Lett. Nuovo Cimento 39 (1984), pp. 315–318. G.F. Torres del Castillo and I. Rubalcava Garcı´a, Hamiltonians and lagrangians of nonautonomous one-dimensional mechanical systems, Rev. Mexicana Fís. 52 (2006), pp. 429–432. S. Smale, Topology and mechanics I, Invent. Math. 10 (1970), pp. 305–331. S. Smale, Topology and mechanics II. The planar n-body problem, Invent. Math. 11 (1970), pp. 45–64. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer- Verlag, New York, Berlin, 1983. V.I. Arnold, Dynamical Systems III, Springer-Verlag, Berlin, 1993. J. Patera and P. Winternitz, Invariant trilinear couplings involving both SU(2) and SU(1, 1) states, J. Math. Phys. 14 (1973), pp. 1977–1983. C. Boyer, E. Kalnins, and W. Miller, Lie theory and separation of variables VI. The equation iUtþD2U¼0, J. Math. Phys. 16 (1975), pp. 499–511 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 134ad262-ecde-4097-bca7-ddaead91ce52 | |
| relation.isAuthorOfPublication.latestForDiscovery | 134ad262-ecde-4097-bca7-ddaead91ce52 |
Download
Original bundle
1 - 1 of 1