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dc.contributor.authorViswanath, Divakaren_US
dc.date.accessioned2006-12-19T19:12:08Z
dc.date.available2006-12-19T19:12:08Z
dc.date.issued2003-05-01en_US
dc.identifier.citationViswanath, Divakar (2003). "Symbolic dynamics and periodic orbits of the Lorenz attractor*." Nonlinearity. 16(3): 1035-1056. <http://hdl.handle.net/2027.42/49072>en_US
dc.identifier.issn0951-7715en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/49072
dc.description.abstractThe butterfly-like Lorenz attractor is one of the best known images of chaos. The computations in this paper exploit symbolic dynamics and other basic notions of hyperbolicity theory to take apart the Lorenz attractor using periodic orbits. We compute all 111011 periodic orbits corresponding to symbol sequences of length 20 or less, periodic orbits whose symbol sequences have hundreds of symbols, the Cantor leaves of the Lorenz attractor, and periodic orbits close to the saddle at the origin. We derive a method for computing periodic orbits as close as machine precision allows to a given point on the Lorenz attractor. This method gives an algorithmic realization of a basic hypothesis of hyperbolicity theory—namely, the density of periodic orbits in hyperbolic invariant sets. All periodic orbits are computed with 14 accurate digits.en_US
dc.format.extent3118 bytes
dc.format.extent854244 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherIOP Publishing Ltden_US
dc.titleSymbolic dynamics and periodic orbits of the Lorenz attractor*en_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, MI 48109-1109, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/49072/2/no3314.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1088/0951-7715/16/3/314en_US
dc.identifier.sourceNonlinearity.en_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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