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Integrability of Nonholonomic Heisenberg Type Systems
Symmetry, Integrability and Geometry: Methods and Applications
We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical r-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.doi:10.3842/sigma.2016.112 fatcat:6wn6y5pmibgc7plx6svcmu67xu