On integrability of certain rank 2 sub-Riemannian structures

0485783 - ASÚ 2018 RIV RU eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GJ17-06962Y
Institucionální podpora: RVO:67985815
Klíčová slova: sub-Riemannian geodesic flow * Killing tensor * integral
Obor OECD: Astronomy (including astrophysics,space science)
Impakt faktor: 1.383, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0280723