A nonintegrable sub-Riemannian geodesic flow on a Carnot group

zbMath0941.53046MaRDI QIDQ1972760

Richard Montgomery, Michael Shapiro, Alexander Stolin

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

zbMATH Keywords

HamiltonianCarnot groupsub-Riemannian geodesic flow

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (12)

Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups ⋮ Control of the motion of a helical body in a fluid using rotors ⋮ Non-integrable sub-Riemannian geodesic flow on \(J^2(\mathbb{R}^2,\mathbb{R})\) ⋮ On integrability of certain rank 2 sub-Riemannian structures ⋮ Anisotropic quaternion Carnot groups: Geometric analysis and Green function ⋮ On the complete integrability of the geodesic flow of pseudo-\(H\)-type Lie groups ⋮ Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Symmetric Killing tensors on nilmanifolds ⋮ Integrability of left-invariant sub-Riemannian structures on the special linear group \(\mathrm{SL}_2(\mathbb R)\) ⋮ Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

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