Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf fibration

@article{Roa2016StabilityAC,
  title={Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf fibration},
  author={Javier Roa and Hodei Urrutxua and Jes'us Pel'aez},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2016},
  volume={459},
  pages={2444-2454}
}
The need for the extra dimension in Kustaanheimo–Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a four-dimensional manifold called the fundamental manifold. Based on geometric and topological aspects classical concepts of stability are translated to KS language. The separation between manifolds of solutions generalizes the concept of Lyapunov stability. The… 

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