Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/98226
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dc.contributor.CRUESPUNIVERSIDADE DE ESTADUAL DE CAMPINASpt_BR
dc.identifier.isbnpt
dc.typeArtigo de periódicopt_BR
dc.titleAnalytical Determination Of Unstable Periodic Orbits In Area Preserving Mapspt_BR
dc.contributor.authorDa Silva Ritter G.L.pt_BR
dc.contributor.authorOzorio De Almeida A.M.pt_BR
dc.contributor.authorDouady R.pt_BR
unicamp.authorDa Silva Ritter, G.L., Instituto de Física, UNICAMP, Campinas, 13081 SP, Brazilpt_BR
unicamp.authorOzorio De Almeida, A.M., Instituto de Física, UNICAMP, Campinas, 13081 SP, Brazilpt_BR
unicamp.author.externalDouady, R., Centre de Mathématiques, Ecole Polytechnique, 91128 Palaiseau Cedex, Francept
dc.description.abstractThe Birkhoff normal form, for the neighbourhood of an unstable fixed point of an analytical area preserving map, was proved by Moser to converge. We here show that the region of convergence in fact stretches along a narrow strip surrounding the stable and the unstable manifolds. Consequently the normal form can be used to compute homoclinic points and unstable periodic orbit families that accumulate on them. This is verified for quadratic maps: we find unstable orbits which return to themselves within an accuracy of twenty-one significant figures. A pair of linear equations is derived, which supply approximately all the periodic orbits accumulating on a given homoclinic point. This explicit formula is asymptotically valid in the limit of large periods. © 1987.en
dc.relation.ispartofPhysica D: Nonlinear Phenomenapt_BR
dc.publisherpt_BR
dc.date.issued1987pt_BR
dc.identifier.citationPhysica D: Nonlinear Phenomena. , v. 29, n. 1-2, p. 181 - 190, 1987.pt_BR
dc.language.isoenpt_BR
dc.description.volume29pt_BR
dc.description.issuenumber1-2pt_BR
dc.description.initialpage181pt_BR
dc.description.lastpage190pt_BR
dc.rightsfechadopt_BR
dc.sourceScopuspt_BR
dc.identifier.issn1672789pt_BR
dc.identifier.doi10.1016/0167-2789(87)90054-6pt_BR
dc.identifier.urlhttp://www.scopus.com/inward/record.url?eid=2-s2.0-0038941340&partnerID=40&md5=293e4fc3b5587e1f72ea20669eb64382pt_BR
dc.date.available2015-06-30T13:41:02Z
dc.date.available2015-11-26T14:37:10Z-
dc.date.accessioned2015-06-30T13:41:02Z
dc.date.accessioned2015-11-26T14:37:10Z-
dc.description.provenanceMade available in DSpace on 2015-06-30T13:41:02Z (GMT). No. of bitstreams: 1 2-s2.0-0038941340.pdf: 605535 bytes, checksum: 126b7a3117ceccf93cfc276d2acce915 (MD5) Previous issue date: 1987en
dc.description.provenanceMade available in DSpace on 2015-11-26T14:37:10Z (GMT). No. of bitstreams: 1 2-s2.0-0038941340.pdf: 605535 bytes, checksum: 126b7a3117ceccf93cfc276d2acce915 (MD5) Previous issue date: 1987en
dc.identifier.urihttp://www.repositorio.unicamp.br/handle/REPOSIP/98226
dc.identifier.urihttp://repositorio.unicamp.br/jspui/handle/REPOSIP/98226-
dc.identifier.idScopus2-s2.0-0038941340pt_BR
dc.description.referenceBirkhoff, (1920) Acta Math., 43, p. 1pt_BR
dc.description.referenceArnol'd, (1982) Geometrical Methods in the Theory of Ordinary Differential Equtions, , Springer, New Yorkpt_BR
dc.description.referenceMoser, (1956) Communications on Pure and Applied Mathematics, 9, p. 673pt_BR
dc.description.referencede Almeida, Coutinho, da Silva Ritter, (1985) Rev. Bras. Fis., 15, p. 60pt_BR
dc.description.referenceChurchill, (1960) Complex Variables and Applications, , McGraw-Hill, New Yorkpt_BR
dc.description.referenceBirkhoff, (1927) Acta. Math., 50, p. 359pt_BR
dc.description.referenceGuckenheimer, Holmes, (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, , Springer, New Yorkpt_BR
dc.description.referenceHenon, (1969) Q. Appl. Math., 27, p. 291pt_BR
dc.description.referenceBountis, (1981) Physica, 3 D, p. 577pt_BR
dc.description.referenceda Silva Ritter, (1986) Master's Thesis, , Unicamppt_BR
dc.description.referenceGreene, (1979) Journal of Mathematical Physics, 20, p. 1183pt_BR
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