# 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} }

## 12 Citations

Linear instability for periodic orbits of non-autonomous Lagrangian systems

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- 2019

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the…

An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian n-body Problem

- Mathematics
- 2021

In the Newtonian n-body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic results about their Morse…

Minimal collision arcs asymptotic to central configurations

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- 2020

We are concerned with the analysis of finite time collision trajectories for a class of singular anisotropic homogeneous potentials of degree $-\alpha$, with $\alpha\in(0,2)$ and their lower order…

Index theory for heteroclinic orbits of Hamiltonian systems

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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…

An Index Theory for Singular Solutions of the Newtonian $n$-body Problem

- Mathematics
- 2019

In the Newtonian $n$-body problem, for solutions with arbitrary energy, that start and end either at infinity or total collision, we prove some basic results about their Morse and Maslov indices.…

Parabolic orbits in Celestial Mechanics: a functional‐analytic approach

- MathematicsProceedings of the London Mathematical Society
- 2021

We prove the existence of half‐entire parabolic solutions, asymptotic to a prescribed central configuration, for the equation ẍ=∇U(x)+∇W(t,x),x∈Rd,where d⩾2 , U is a positive and positively…

An Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem

- Physics, MathematicsCommunications in Mathematical Physics
- 2018

In the variational study of singular Lagrange systems, the zero energy solutions play an important role. The anisotropic Kepler problem is such a singular system introduced by physicist M. Gutzwiller…

Application of Morse index in weak force N-body problem

- MathematicsNonlinearity
- 2019

Due to collision singularities, the Lagrange action functional of the N-body problem in general is not differentiable. Because of this, the usual critical point theory can not be applied to this…

Bifurcation of heteroclinic orbits via an index theory

- MathematicsMathematische Zeitschrift
- 2018

Heteroclinic orbits for one-parameter families of nonautonomous vectorfields appear in a very natural way in many physical applications. Inspired by a recent bifurcation result for homoclinic…

Free time minimizers for the three-body problem

- Mathematics
- 2018

Free time minimizers of the action (called “semi-static” solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120–131, 1996) play a…

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Index theory for heteroclinic orbits of Hamiltonian systems

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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…

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