Geometrical Obstruction to the Integrability of Geodesic Flows: an Application to the Anisotropic Kepler Problem

Details Geometrical Obstruction to the Integrability of Geodesic Flows: an Application to the Anisotropic Kepler Problem Geometrical Obstruction to the Integrability of Geodesic Flows: an Application to the Anisotropic Kepler Problem

2002-02-23

arxiv.org/abs/nlin/0202051v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, no figures

Scientific paper

Resorting to classical techniques of Riemannian geometry we develop a
geometrical method suitable to investigate the nonintegrability of geodesic
flows and of natural Hamiltonian systems. Then we apply such method to the
Anisotropic Kepler Problem (AKP) and we prove that it is not analytically
integrable.

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