Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants
In the framework of the spatial circular Hill three-body problem, we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbits families. The extensive collection of families within this problem constitutes a complex network, fundamentally compr...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
13 March 2025
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| In: |
Celestial mechanics and dynamical astronomy
Year: 2025, Volume: 137, Pages: 1-77 |
| ISSN: | 1572-9478 |
| DOI: | 10.1007/s10569-025-10241-7 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10569-025-10241-7
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| Author Notes: | Cengiz Aydin, Alexander Batkhin |
| Summary: | In the framework of the spatial circular Hill three-body problem, we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbits families. The extensive collection of families within this problem constitutes a complex network, fundamentally comprising the so-called basic families of periodic solutions, including the orbits of the satellite g, f, the libration (Lyapunov) a, c, and collision $${\mathscr {B}}_0$$families. Since the Conley-Zehnder index leads to a grading on the local Floer homology and its Euler characteristics, a bifurcation invariant, the computation of those indices facilitates the construction of well-organized bifurcation graphs depicting the interconnectedness among families of periodic solutions. The critical importance of the symmetries of periodic solutions in comprehending the interaction among these families is demonstrated. |
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| Item Description: | Online verfügbar: 13. März 2025 Gesehen am 07.08.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1572-9478 |
| DOI: | 10.1007/s10569-025-10241-7 |