Some problems in the theory of open dynamical systems and deterministic walks in random environments

dc.contributor.advisor Bunimovich, Leonid
dc.contributor.author Yurchenko, Aleksey en_US
dc.contributor.committeeMember Bakhtin, Yuri
dc.contributor.committeeMember Cvitanovic, Predrag
dc.contributor.committeeMember Houdre, Christian
dc.contributor.committeeMember Weiss, Howard
dc.contributor.department Mathematics en_US
dc.date.accessioned 2009-01-22T15:44:59Z
dc.date.available 2009-01-22T15:44:59Z
dc.date.issued 2008-11-11 en_US
dc.description.abstract The 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.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/26549
dc.publisher Georgia Institute of Technology en_US
dc.subject Open dynamical systems en_US
dc.subject Escape rate en_US
dc.subject Autocorrelation function en_US
dc.subject Dynamical systems en_US
dc.subject Holes en_US
dc.subject.lcsh Dynamics
dc.subject.lcsh Chaotic behavior in systems
dc.title Some problems in the theory of open dynamical systems and deterministic walks in random environments en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Bunimovich, Leonid
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication 8385d52f-b627-4839-8603-2683ea2daa55
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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