1,234 research outputs found
Periodic orbits close to elliptic tori and applications to the three-body problem
We prove, under suitable non-resonance and non-degeneracy ``twist''
conditions, a Birkhoff-Lewis type result showing the existence of infinitely
many periodic solutions, with larger and larger minimal period, accumulating
onto elliptic invariant tori (of Hamiltonian systems). We prove the
applicability of this result to the spatial planetary three-body problem in the
small eccentricity-inclination regime. Furthermore, we find other periodic
orbits under some restrictions on the period and the masses of the ``planets''.
The proofs are based on averaging theory, KAM theory and variational methods.
(Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential
Equations.
Stability Properties of the Riemann Ellipsoids
We study the ellipticity and the ``Nekhoroshev stability'' (stability
properties for finite, but very long, time scales) of the Riemann ellipsoids.
We provide numerical evidence that the regions of ellipticity of the ellipsoids
of types II and III are larger than those found by Chandrasekhar in the 60's
and that all Riemann ellipsoids, except a finite number of codimension one
subfamilies, are Nekhoroshev--stable. We base our analysis on a Hamiltonian
formulation of the problem on a covering space, using recent results from
Hamiltonian perturbation theory.Comment: 29 pages, 6 figure
GCD matrices, posets, and nonintersecting paths
We show that with any finite partially ordered set one can associate a matrix
whose determinant factors nicely. As corollaries, we obtain a number of results
in the literature about GCD matrices and their relatives. Our main theorem is
proved combinatorially using nonintersecting paths in a directed graph.Comment: 10 pages, see related papers at http://www.math.msu.edu/~saga
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