Show simple item record

dc.contributor.authorYurchenko, Alekseyen_US
dc.date.accessioned2009-01-22T15:44:59Z
dc.date.available2009-01-22T15:44:59Z
dc.date.issued2008-11-11en_US
dc.identifier.urihttp://hdl.handle.net/1853/26549
dc.description.abstractThe first part of this work deals with open dynamical systems. A natural question of how the survival probability depends upon a position of a hole was seemingly never addresses in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period), which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole. In the second part we consider some classes of cellular automata called Deterministic Walks in Random Environments on Z^1. At first we deal with the system with constant rigidity and Markovian distribution of scatterers on Z^1. It is shown that these systems have essentially the same properties as DWRE on Z^1 with constant rigidity and independently distributed scatterers. Lastly, we consider a system with non-constant rigidity (so called process of aging) and independent distribution of scatterers. Asymptotic laws for the dynamics of perturbations propagating in such environments with aging are obtained.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectOpen dynamical systemsen_US
dc.subjectEscape rateen_US
dc.subjectAutocorrelation functionen_US
dc.subjectDynamical systemsen_US
dc.subjectHolesen_US
dc.subject.lcshDynamics
dc.subject.lcshChaotic behavior in systems
dc.titleSome problems in the theory of open dynamical systems and deterministic walks in random environmentsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Bunimovich, Leonid; Committee Member: Bakhtin, Yuri; Committee Member: Cvitanovic, Predrag; Committee Member: Houdre, Christian; Committee Member: Weiss, Howarden_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record