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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
On Integrability of Certain Rank 2 Sub-Riemannian Structures
Boris S. Kruglikova, Andreas Vollmerbc, Georgios Lukes-Gerakopoulosde a Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway
b Mathematisches Institut, Friedrich-Schiller-Universität, 07737 Jena, Germany
c INdAM - Politecnico di Torino, Dipartimento di Scienze Matematiche,
Corso Duca degli Abruzzi 24, 10129 Torino, Italy
d Astronomical Institute of the Academy of Sciences of the Czech Republic, Boční II 1401/1a, CZ-141 31 Prague, Czech Republic
e Institute of Theoretical Physics, Faculty of Mathematics and Physics,
Charles University in Prague, 121 16 Prague, Czech Republic
Аннотация:
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.
Ключевые слова:
Sub-Riemannian geodesic flow, Killing tensor, integral, symmetry, Tanaka prolongation, overdetermined system of PDE, prolongation.
Поступила в редакцию: 31.01.2017 Принята в печать: 15.08.2017
Образец цитирования:
Boris S. Kruglikov, Andreas Vollmer, Georgios Lukes-Gerakopoulos, “On Integrability of Certain Rank 2 Sub-Riemannian Structures”, Regul. Chaotic Dyn., 22:5 (2017), 502–519
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd272 https://www.mathnet.ru/rus/rcd/v22/i5/p502
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