1.
Kilin A. A., Maciejewski A., Mamaev I. S., Przybylska M., Sachkov Y. L.
Abnormal Geodesics for a Carnot Group with Growth Vector $(2, 3, 5, 8, 14)$
Regular and Chaotic Dynamics, 2026, vol. 31, no. 2, pp. 177-224
Abstract
pdf (1.77 Mb)
This paper is concerned with abnormal geodesics on the Carnot group with growth
vector $(2, 3, 5, 8, 14)$. Because of a large number of symmetries, this problem reduces to an
analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the
resulting system are identified. For these cases, first integrals and explicit solutions are found. It
is shown that in the general case the system admits no additional meromorphic first integrals.
The paper concludes by discussing some problems regarding the abnormal geodesics on Lie
groups.
| Keywords: |
Carnot group, Lie algebra, geodesic, integrability, Kovalevskaya method, first integral, quadrature, differential Galois theory, meromorphic first integral, nonintegrability |
| Citation: |
Kilin A. A., Maciejewski A., Mamaev I. S., Przybylska M., Sachkov Y. L., Abnormal Geodesics for a Carnot Group with Growth Vector $(2, 3, 5, 8, 14)$, Regular and Chaotic Dynamics, 2026, vol. 31, no. 2, pp. 177-224 |
| DOI: |
10.1134/S1560354726020012 |
| Full text: |
pdf
(1.77 Mb)
|
Journal Info
| Impact-factor WoS (2022): |
1.400 (Q2) |
| Impact-factor RSCI (2022): |
0.399 (Q2) |
| ISSN (print): |
1560-3547 |
| ISSN (online): |
1468-4845 |
| Site: |
http://rcd.ics.org.ru/ |
