A separation bound for non-Hamiltonian differential equations with proper first integrals
| dc.contributor.author | Gascón, Francisco G. | |
| dc.contributor.author | Peralta Salas, Daniel | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.date.accessioned | 2023-06-20T18:43:05Z | |
| dc.date.available | 2023-06-20T18:43:05Z | |
| dc.date.issued | 2000-05 | |
| dc.description.abstract | It is shown that when a dynamical system X0 with a proper set of global first integrals is perturbed, the phase space region accessible to the orbits of the perturbed vector field X0+Xp is bounded (we are assuming here that the time variable runs over a finite interval). A polynomial new bound is obtained for the separation between the solutions of X0 and X0+Xp. Perturbations near an equilibrium point of X0 are also considered. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20984 | |
| dc.identifier.doi | 10.1063/1.533280 | |
| dc.identifier.issn | 0022-2488 | |
| dc.identifier.officialurl | http://jmp.aip.org/resource/1/jmapaq/v41/i5/p2922_s1 | |
| dc.identifier.relatedurl | http://jmp.aip.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58415 | |
| dc.issue.number | 5 | |
| dc.journal.title | Journal of Mathematical Physics | |
| dc.language.iso | eng | |
| dc.page.final | 2930 | |
| dc.page.initial | 2922 | |
| dc.publisher | American Institute of Physics | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Dynamical system | |
| dc.subject.keyword | global first integrals | |
| dc.subject.keyword | orbits | |
| dc.subject.keyword | equilibrium point | |
| dc.subject.keyword | partial differential equations | |
| dc.subject.keyword | perturbation theory | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | A separation bound for non-Hamiltonian differential equations with proper first integrals | |
| dc.type | journal article | |
| dc.volume.number | 41 | |
| dcterms.references | V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, Berlin, 1980); N. Nekoroshev, Russ. Math. Surv. 32, 1 (1977); S. Coffey, A. Deprit, and B. Miller, Celest. Mech. 39, 365 (1986); A. Celletti and L. Ferrara, ibid. 64, 261 (1996). V. Berbyuk, J. Appl. Math. Mech. 56, 747 (1992). J. Moser, Commun. Pure Appl. Math. 23, 609 (1970). A. Weinstein, Invent. Math. 20, 47 (1973); Bull. Am. Math. Soc. 77, 814 (1971); A. Markeev and A. Sokolski, J. Appl. Math. Mech. 42, 52 (1978). O. Christov, J. Math. Phys. 35, 3448 (1994). J. Duistermaat, Commun. Pure Appl. Math. 33, 687 (1980); E. Stiefel and G. Scheifele, Linear and Regular Celestial Mechanics, (Springer, Berlin, 1971); Y. Hagihara, Celestial Mechanics, Vol. II, Perturbation Theory (MIT, Cambridge, MA, 1972); H. Hestenes, New Foundations of Classical Mechanics (Kluwer, Dordrecht, 1993). E. Barbashin, Introduction to the Theory of Stability (Noorhoff, Groningen, 1970); E. Hille, Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA, 1969). E. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955). V. Kozlov, J. Appl. Math. Mech. 56, 803 (1992); M. Giordaro, G. Marmo, and C. Rubano, Inverse Probl. 9, 443 (1993). L. Landau and E. Lifchitz, Mecanique (MIR, Moscow, 1965); A. Weinstein, Invent. Math. 20, 47 (1973); H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1965). Y. Chouquet-Bruhat, C. DeWitt-Morette, and M. Dillard, Analysis, Manifolds and Physics (North Holland, Amsterdam, 1978). J. Bochnak, M. Coste, and M. F. Roy, Geometrie Algebraic Reelle (Springer, Berlin, 1987). R. Narasimhan, Analysis on Real and Complex Manifolds, Adv. Studies in Pure Math. 1 (North Holland, Amsterdam, 1968). R. Thom, Commun. Math. Helv. 123, 17 (1954). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a6d5c814-2809-4e3f-9994-64085621a568 | |
| relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
| relation.isAuthorOfPublication.latestForDiscovery | a6d5c814-2809-4e3f-9994-64085621a568 |
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