Integrability of magnetic geodesic flows
| dc.contributor.author | Naqvi, Syeda Atika Batool | |
| dc.contributor.examiningcommittee | Cowan, Craig (Mathematics) Portet, Stephanie (Mathematics) | en_US |
| dc.contributor.supervisor | Butler, Leo T. (Mathematics) | en_US |
| dc.date.accessioned | 2020-04-06T20:00:58Z | |
| dc.date.available | 2020-04-06T20:00:58Z | |
| dc.date.copyright | 2020-04-01 | |
| dc.date.issued | 2020-03-31 | en_US |
| dc.date.submitted | 2020-04-01T16:45:05Z | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | This thesis investigates some aspects of the integrability problem of a Hamiltonian system. The Hamiltonian system with Hamiltonian function H = Xn i,j=1 1 2gij(x1, . . . , xn)pipj , describes the geodesic flow of a Riemannian metric ds2 = Pn i,j=1 gij(x1, . . . , xn)dxidxj on an n-dimensional manifold. Some results from the research article, Polynomials integrals of magnetic geodesic flows on the 2-torus on several energy levels [3], are studied. In particular, a complex structure on the 2-torus is constructed to prove that if the geodesic flow with non-zero magnetic field on the 2-torus admits an additional cubic-in-momenta first integral on two different energy levels, then the magnetic field and the metric are functions of one variable. | en_US |
| dc.description.note | May 2020 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/34651 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Integrability of magnetic geodesic flows | en_US |
| dc.type | master thesis | en_US |