Integrability versus topology of configuration manifolds and domains of possible motions

2005/01/24 by M. Rudnev, Rudnev, M., V. Ten +1
Mathematics · #37J30 #37J35 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37J30 #msc:37J35

paper · pdf · doi:10.48550/arxiv.math/0501413

arxiv created 2005/01/24 · arxiv updated 2009/12/01

Abstract

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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