39 citations · 47 across the 10 of their papers we have counts for
11 papers
Noise and dissipation in rigid body motion
Alexis Arnaudon, Alex L. De Castro, Darryl D. Holm
Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: i) a geometric variational motivation for the noise struc…
A coarse stratification of the monster tower
Alex Castro, Susan Jane Colley, Gary Kennedy +1
The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a n…
Noise and dissipation on coadjoint orbits
Alexis Arnaudon, Alex L. Castro, Darryl D. Holm
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symme…
Complete spelling rules for the Monster tower over three-space
Alex L Castro, Wyatt Howard, Corey Shanbrom
The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projec…
Bridges Between Subriemannian Geometry and Algebraic Geometry
Alex L Castro, Wyatt Howard, Corey Shanbrom
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 unrela…
Spelling Rules for the Monster/Semple Tower
Alex L. Castro, Wyatt C. Howard
We further study the incidence relations that arise from the various subtowers, known as Baby Monster, which exist within the -Monster Tower. This allows us to comp…
A Semple Approach to Goursat: The Multi-Flag Case
Alex Castro, Wyatt Howard
In this note we summarize our results from earlier work with the Monster Tower (A Monster Tower Approach to Goursat Multi-Flags). In particular, we give an overview of the problem…
The Geometry of Radiative Transfer
Christian Lessig, Alex L. Castro
We present the geometry and symmetries of radiative transfer theory. Our geometrization exploits recent work in the literature that enables to obtain the Hamiltonian formulation of…
A Monster Tower Approach to Goursat Multi-Flags
Alex L. Castro, Wyatt C. Howard
We consider here the problem of classifying orbits of an action of the dif- feomorphism group of 3-space on a tower of fibrations with P2-fibers that generalize the Monster Tower d…
Curve Singularities and Monster / Semple Towers
Alex L. Castro, Richard Montgomery
In earlier work, we introduced the `Monster tower', a tower of fibrations associated to planar curves. We constructed an algorithm for classifying its points with respect to the eq…
The Chains of Left-invariant CR-structures on SU(2)
Alex L. Castro, Richard Montgomery
We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus . For the standard structur…