In 1998 the Swedish mathematician Warwick Tucker used rigorous interval arithmetic and normal form theory to prove the existence of a strange attractor in the Lorenz system. In large parts, that proof consists of computations implemented and performed on a computer. This thesis is an independent numerical verification of the result obtained by Warwick Tucker, as well as a study of a higher-dimensional system of ordinary differential equations introduced by the Swedish physicist Lennart Stenflo. The same type of mapping data as Warwick Tucker obtained is calculated here via a combination of numerical integration, solving optimisation problems and a coordinate change that brings the system to a normal form around the stationary point in the origin. This data is collected in a graph and the problem of determining the existence of a strange attractor is translated to a few graph theoretical problems. The end result, after the numerical study, is a support for the conclusion that the attractor set of the Lorenz system is a strange attractor and also for the conclusion that the Lorenz-Stenflo system possesses a strange attractor. / QC 20101007
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-172 |
| Date | January 2005 |
| Creators | Ekola, Tommy |
| Publisher | KTH, Matematik (Inst.), Stockholm : KTH |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, monograph, info:eu-repo/semantics/doctoralThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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