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On the singularities of generalized solutions to --body type problems
Vivina Barutello, Davide L. Ferrario, Susanna Terracini
The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical --bo…
Morse index properties of colliding solutions to the -body problem
Vivina Barutello, Simone Secchi
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical --body problem. We introduce a variational Morse--l…
Symmetry groups of the planar 3-body problem and action--minimizing trajectories
Vivina Barutello, Davide L. Ferrario, Susanna Terracini
We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of the equivariant calculus of variations. First, we s…
Action minimizing orbits in the n-body problem with simple choreography constraint
Vivina Barutello, Susanna Terracini
In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight sha…