34 citations · 50 across the 12 of their papers we have counts for
5 papers · 1 filter
The Integrability of a knife-edge Billiard in a Disk
Alejandro Bravo-Doddoli, Huaidian Hou, William Clark +1
This paper proves the integrability of a nonholonomic billiard defined by a knife-edge in a disk. The paper begins by parametrizing the impact space using coordinates that reveal t…
Chaotic subRiemannian geodesic flow in
Alejandro Bravo-Doddoli
The space of -jets of a real function of two real variables, denoted by , admits the structure of a metabelian Carnot group, so $J^2(\mathbb{R}^2,\…
No Periodic normal Geodesics in
Alejandro Bravo-Doddoli
The space of -jets of real function of one real variable admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamilt…
No Periodic Geodesics in Jet Space
Alejandro Bravo-Doddoli
The space of -jets of a real function of one real variable admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, a…
Higher Elastica: Geodesics in the Jet Space
Alejandro Bravo-Doddoli
Carnot groups are subRiemannian manifolds. As such they admit geodesic flows, which are left-invariant Hamiltonian flows on their cotangent bundles. Some of these flows are integra…