| Abstract: |
| One of the key questions on the origin of Jovian irregular satellites,
characterized by their highly eccentric orbit and small mass, is how
they are transferred to the present place. These satellite are believed to be
captured by Jupiter, rather than formed in situ. We employ Lyapunov periodic
orbits (LOs) as a formal definition of the vicinity of Jupiter and
numerically track the orbital distribution of the invarianet manifold of a LO,
varying Jacobi constant $C_J$. The numerical tracking of the manifold is
carried out directly via repeated Poincar\`e mapping of points initially allocated
densely on a fragment of the manifolds near the fixed points, with the
assistance of MPFR multiprecision arithmetics. The numerical computations
shows that the distribution of semi-major
axis of points on the manifolds are quite heavy tailed while its median spans
roughly 1-2x the Jovian orbital radius. |
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