Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic controls in step 2 sub-Finsler problems   We consider control-linear left-invariant time-optimal problems on step 2
Carnot groups with strictly convex set of control parameters (in particular,
sub-Finsler problems).
  We describe all linear-in-momenta Casimirs on the dual of the Lie algebra.
  In the case of rank 3 Lie groups we describe the symplectic foliation on the
dual of the Lie algebra. On this basis we show that extremal controls are
either constant or periodic.
  Some related results for other Carnot groups are presented.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph