Title:
Billiards and statistical mechanics

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dc.contributor.advisor Bunimovich, Leonid
dc.contributor.author Grigo, Alexander en_US
dc.contributor.committeeMember Bonetto, Federico
dc.contributor.committeeMember Chow, Shui-Nee
dc.contributor.committeeMember Cvitanovic, Predrag
dc.contributor.committeeMember Weiss, Howard
dc.contributor.department Mathematics en_US
dc.date.accessioned 2009-08-26T17:30:41Z
dc.date.available 2009-08-26T17:30:41Z
dc.date.issued 2009-05-18 en_US
dc.description.abstract In this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise in the context of hard sphere systems when only one or two spheres are present. In particular we investigate the possibility of elliptic periodic orbits in the general construction of hyperbolic billiards. We show that if non-absolutely focusing components are present there can be elliptic periodic orbits with arbitrarily long free paths. Furthermore, we show that smooth stadium like billiards have elliptic periodic orbits for a large range of separation distances. In the second part we consider hard sphere systems with a large number of particles, which we model by the Boltzmann equation. We develop a new approach to derive hydrodynamic limits, which is based on classical methods of geometric singular perturbation theory of ordinary differential equations. This method provides new geometric and dynamical interpretations of hydrodynamic limits, in particular, for the of the dissipative Boltzmann equation. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/29610
dc.publisher Georgia Institute of Technology en_US
dc.subject Billiards en_US
dc.subject Boltzmann equation en_US
dc.subject.lcsh Hamiltonian systems
dc.subject.lcsh Statistical mechanics
dc.subject.lcsh Ergodic theory
dc.subject.lcsh Dynamics
dc.subject.lcsh Transport theory
dc.title Billiards and statistical mechanics 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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