Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/98226
Type: Artigo de periódico
Title: Analytical Determination Of Unstable Periodic Orbits In Area Preserving Maps
Author: Da Silva Ritter G.L.
Ozorio De Almeida A.M.
Douady R.
Abstract: The 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.
Editor: 
Rights: fechado
Identifier DOI: 10.1016/0167-2789(87)90054-6
Address: http://www.scopus.com/inward/record.url?eid=2-s2.0-0038941340&partnerID=40&md5=293e4fc3b5587e1f72ea20669eb64382
Date Issue: 1987
Appears in Collections:Unicamp - Artigos e Outros Documentos

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