Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants
Cengiz Aydin
Heidelberg University
In this talk I discuss the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families in the framework of the spatial circular Hill three-body problem. 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, halo and collision B0 families. The symplectic tools include computation of Conley-Zehnder index, Krein signature, and local Floer homology (graded by Conley-Zehnder indices) and its Euler characteristics. Since the latter is a bifurcation invariant, the computation of Conley-Zehnder indices facilitates the construction of well-organized bifurcation graphs depicting the interconnectedness among families of periodic solutions. In addition, I demonstrate how to express lunar months in terms of Conley-Zehnder indices, Krein signatures and Floquet multipliers associated to Hill's lunar orbit.