Symbolic dynamics and periodic orbits of the Lorenz attractor*
dc.contributor.author | Viswanath, Divakar | en_US |
dc.date.accessioned | 2006-12-19T19:12:08Z | |
dc.date.available | 2006-12-19T19:12:08Z | |
dc.date.issued | 2003-05-01 | en_US |
dc.identifier.citation | Viswanath, 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.issn | 0951-7715 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/49072 | |
dc.description.abstract | The 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.extent | 3118 bytes | |
dc.format.extent | 854244 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.publisher | IOP Publishing Ltd | en_US |
dc.title | Symbolic dynamics and periodic orbits of the Lorenz attractor* | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, MI 48109-1109, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/49072/2/no3314.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1088/0951-7715/16/3/314 | en_US |
dc.identifier.source | Nonlinearity. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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