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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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Bibliographic Details
Main Authors: Aydin, Cengiz (Author) , Batkhin, Alexander (Author)
Format: Article (Journal)
Language:English
Published: 13 March 2025
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

MARC

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520 |a 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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