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arXiv · 2410.21245

Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants

Cengiz Aydin·Alexander Batkhin
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Abstract

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 orbit 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 $\mathcal B_0$ 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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Cengiz Aydin, Alexander Batkhin. 2025-01-30. Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants. https://arxiv.org/abs/2410.21245

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