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Through symmetry breaking to higher dimensional chaotic scattering

Merlo, Olivier. Through symmetry breaking to higher dimensional chaotic scattering. 2004, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_7024

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Abstract

The goal of this thesis is to gain some insight into chaotic scattering dynamics in
systems with more than two effective degrees of freedom. We use the idea of "gradually"
introducing another degree of freedom by perturbating slightly a symmetry
that has reduced a three–dimensional system to two effective dimensions.
We furthermore specifically study the case of a system where a particle was scattered
by a hard disc moving on a circle which will be slightly deformed to an
ellipse. This leads to a slight violation of the Jacobi integral which causes the increase
of dimension of phase space.
We first complement previous studies of the problem with symmetry by showing
elliptic areas, obtaining linear response results and the bifurcation scenario.
Then we show how analyzing spaces of initial conditions in terms of the number
of the scattering events before ejection yields information about periodic orbits,
stable or longlived islands and bifurcations. This allows us to gain considerable
insight into the scattering process, that can be of use in qualitative understanding
of planetary rings in celestial mechanics and seems to be valid far beyond the toy
model we use.
Advisors:Trautmann, Dirk
Committee Members:Seligman, Thomas H.
Faculties and Departments:05 Faculty of Science > Departement Physik > Former Organization Units Physics > Atomphysik (Trautmann)
UniBasel Contributors:Trautmann, Dirk
Item Type:Thesis
Thesis Subtype:Doctoral Thesis
Thesis no:7024
Thesis status:Complete
Bibsysno:Link to catalogue
Number of Pages:72
Language:English
Identification Number:
Last Modified:22 Jan 2018 15:50
Deposited On:13 Feb 2009 15:03

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