Title:
How well can one resolve the state space of a chaotic map?

dc.contributor.advisor Cvitanović, Predrag
dc.contributor.author Lippolis, Domenico en_US
dc.contributor.committeeMember Bellissard, Jean
dc.contributor.committeeMember Weiss, Howard
dc.contributor.committeeMember Wiesenfeld, Kurt
dc.contributor.committeeMember Zhou, Hao Min
dc.contributor.department Physics en_US
dc.date.accessioned 2010-06-10T15:20:13Z
dc.date.available 2010-06-10T15:20:13Z
dc.date.issued 2010-04-06 en_US
dc.description.abstract All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching/contraction and the smearing due to noise. My goal is to determine the `finest attainable' partition for a given hyperbolic dynamical system and a given weak additive white noise. That is achieved by computing the local eigenfunctions of the Fokker-Planck evolution operator in linearized neighborhoods of the periodic orbits of the corresponding deterministic system, and using overlaps of their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. The method applies in principle to both continuous- and discrete-time dynamical systems. Numerical tests of such optimal partitions on unimodal maps support my hypothesis. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/33841
dc.publisher Georgia Institute of Technology en_US
dc.subject Symbolic dynamics en_US
dc.subject Noise en_US
dc.subject Chaos en_US
dc.subject Periodic orbits. en_US
dc.subject.lcsh State-space methods
dc.subject.lcsh Dynamics
dc.subject.lcsh Partitions (Mathematics)
dc.subject.lcsh Stochastic analysis
dc.title How well can one resolve the state space of a chaotic map? en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Cvitanović, Predrag
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Physics
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relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 2ba39017-11f1-40f4-9bc5-66f17b8f1539
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