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dc.contributor.advisorMartens, Marcoen_US
dc.contributor.authorNam, Young Wooen_US
dc.contributor.otherDepartment of Mathematicsen_US
dc.date.accessioned2013-05-22T17:35:18Z
dc.date.available2013-05-22T17:35:18Z
dc.date.issued1-Dec-11en_US
dc.date.submitted11-Decen_US
dc.identifierNam_grad.sunysb_0771E_10781en_US
dc.identifier.urihttp://hdl.handle.net/1951/59802
dc.description194 pg.en_US
dc.description.abstractThe three dimensional H??non-like map is defined on the cubic box domain. The geometric properties of Cantor attractor of F are studied. The Jacobian determinant of nth renormalized map is expressed asymptotically using the universal map. The set of the model maps, M is invariant class under renormalization. If there exist C^r invariant surfaces under model maps, then the geometric properties of Cantor attractor of F in M is involved with the same properties for the two dimensional H??non-like map. In particular, the non rigidity and the typical unbounded geometry of Cantor attractor are proved. Another invariant class under renormalization, N is defined by the particular equation of partial derivatives of third coordinate map of F. In contrast with the maps in M, the result of two dimensional H??non renormalization is not applied to the map in N. Instead the non linear scaling maps are analyzed in a direct way with recursive formulas. However, same geometric properties of Cantor attractor, in particular, non rigidity and typical unbounded geometry are also proved for the map in the class N.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Mathematics. Charles Taber (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshMathematicsen_US
dc.subject.otherCantor attractor, Henon map, renormalization, unbounded geometry, universalityen_US
dc.titleRenormalization of three dimensional H??non mapen_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Martens, Marco . Committee Member(s): Lyubich, Mikhail ; Schul, Ranaan ; Tresser, Charles.en_US
dc.mimetypeApplication/PDFen_US


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