Lagrangian Rabinowitz Floer Homology and its application to powered flyby orbits in the restricted three body problem
- In this thesis we use an equivariant version of Lagrangian Rabinowitz Floer homology to show the existence of infinitely many symmetric consecutive collision orbits in the restricted three body problem for all energies below the first critical energy value. Using Levi-Civita regularization in the planar case and Kustaanheimo-Stiefel regularization in the spatial case allows us to distinguish between orbits passing through a solar eclipse point or a lunar eclipse point and prove the above existence statement for both of them separately. To calculate this homology we show that under certain conditions the G-equivariant Lagrangian Rabinowitz Floer homology is equal to the Tate homology of G.
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| Author: | Kevin RuckORCiD |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1108689 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/110868 |
| Advisor: | Urs Frauenfelder |
| Type: | Doctoral Thesis |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2023/12/06 |
| Release Date: | 2024/03/06 |
| Tag: | Symplectic Topology; Three Body Problem; Rabinowitz Floer Homology |
| GND-Keyword: | Eingeschränktes Dreikörperproblem; Homologie; Orbit <Mathematik>; Symplektische Geometrie |
| Pagenumber: | 75 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Analysis und Geometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY-NC 4.0: Creative Commons: Namensnennung - Nicht kommerziell (mit Print on Demand) |
