Results 11 to 20 of about 479 (34)
Numerical Methods and Closed Orbits in the Kepler-Heisenberg Problem
, 2017 The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental ...
Dods, Victor, Shanbrom, Corey
core +1 more source
Nos\'e-Thermostated Mechanical Systems on the n-Torus
, 2017 Let $H(q,p) = \frac12 | p |^2 + V(q)$ be an $n$-degree of freedom $C^r$ mechanical Hamiltonian on the cotangent bundle of the $n$-torus where $r>2n+2$. When the metric $| * |$ is flat, the Nos\'e-thermostated system associated to $H$ is shown to have a ...
Butler, Leo T.
core +1 more source
A counterexample to gluing theorems for MCP metric measure spaces
, 2018 Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq \kappa$ is an Alexandrov space with the same dimension and satisfying the same curvature lower ...
Rizzi, Luca
core +2 more sources
Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups [PDF]
, 2014 Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liouville integrability and superintegrability are ...
Mashtakov, Alexey P., Sachkov, Yuri L.
core +1 more source
, 2013 We study the classification of area-stationary and stable $C^2$ regular surfaces in the space of the rigid motions of the Minkowski plane E(1,1), equipped with its sub-Riemannian structure.
Galli, Matteo
core +1 more source
Riemannian and Sub-Riemannian geodesic flows
, 2015 In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of
Grong, Erlend, Molina, Mauricio Godoy
core +1 more source
Bridges Between Subriemannian Geometry and Algebraic Geometry
, 2014 We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes.
Castro, Alex L +2 more
core +1 more source
Invertible Carnot Groups [PDF]
, 2016 We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman, David M.
core
Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 Don S, Magnani V.
europepmc +1 more source
Almost-Riemannian manifolds do not satisfy the curvature-dimension condition. [PDF]
Calc Var Partial Differ Equ, 2023 Magnabosco M, Rossi T.
europepmc +1 more source