Integrability versus topology of configuration manifolds and domains of possible motions

Details Integrability versus topology of configuration manifolds and domains of possible motions Integrability versus topology of configuration manifolds and domains of possible motions

2005-01-24

arxiv.org/abs/math/0501413v1

Mathematics

Dynamical Systems

Scientific paper

We establish a generic sufficient condition for a compact $n$-dimensional
manifold bearing an integrable geodesic flow to be the $n$-torus. As a
complementary result, we show that in the case of domains of possible motions
with boundary, the first Betti number of the domain of possible motions may be
arbitrarily large.

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