# An index theory for asymptotic motions under singular potentials

@article{Barutello2017AnIT,
title={An index theory for asymptotic motions under singular potentials},
author={Vivina L. Barutello and Xijun Hu and Alessandro Portaluri and Susanna Terracini},
journal={arXiv: Dynamical Systems},
year={2017}
}
• Published 3 May 2017
• Mathematics
• arXiv: Dynamical Systems
12 Citations

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## References

SHOWING 1-10 OF 58 REFERENCES
On the singularities of generalized solutions to n-body type problems !
• Mathematics
• 2007
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 N‐body problems with
Index theory for heteroclinic orbits of Hamiltonian systems
• Mathematics
• 2017
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic
Entire parabolic trajectories as minimal phase transitions
• Mathematics
• 2011
For the class of anisotropic Kepler problems in $$\mathbb{R }^d\setminus \{0\}$$ with homogeneous potentials, we seek parabolic trajectories having prescribed asymptotic directions at infinity and
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
• Mathematics
• 2009
In this paper, using the Maslov index theory in symplectic geometry, we build up some stability criteria for symmetric periodic orbits in a Hamiltonian system, which is motivated by the recent
A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• Mathematics
• 2005
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-Riemannian
Morse Index and Linear Stability of the Lagrangian Circular Orbit in a Three-Body-Type Problem Via Index Theory
• Mathematics
• 2014
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter β and on the eccentricity e of the orbit. We