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On integrability of certain rank 2 sub-Riemannian structures
- 1.0485783 - ASÚ 2018 RIV RU eng J - Journal Article
Kruglikov, B.S. - Vollmer, A. - Lukes-Gerakopoulos, Georgios
On integrability of certain rank 2 sub-Riemannian structures.
Regular & Chaotic Dynamics. Roč. 22, č. 5 (2017), s. 502-519. ISSN 1560-3547. E-ISSN 1468-4845
R&D Projects: GA ČR(CZ) GJ17-06962Y
Institutional support: RVO:67985815
Keywords : sub-Riemannian geodesic flow * Killing tensor * integral
OECD category: Astronomy (including astrophysics,space science)
Impact factor: 1.383, year: 2017
We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.
Permanent Link: http://hdl.handle.net/11104/0280723
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