Title: Integrability of left-invariant sub-Riemannian structures on the special linear group 
Authors: A.P. Mashtakov, Yu.L. Sachkov
Journal title: Differential Equations
Year: 2014
Issue: 11
Volume: 50
Pages: 1541–1547
Abstract:
We show that the Hamiltonian system of ordinary differential equations of the Pontryagin maximum principle for left-invariant sub-Riemannian structures of elliptic type on the Lie group SL2(R) is Liouville integrable.
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