Invariant submanifold flows

Invariant Submanifold Flows

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and ob...

The Boundary of an Affine Invariant Submanifold

Invariant submanifold for series arrays of Josephson junctions.

We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current, and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some ...

Gradient Flows on a Riemannian Submanifold for Discrete Tomography

We present a smooth geometric approach to discrete tomography that jointly performs tomographic reconstruction and label assignment. The flow evolves on a submanifold equipped with a Hessian Riemannian metric and properly takes into account given projection constraints. The metric naturally extends the Fisher-Rao metric from labeling problems with directly observed data to the inverse problem o...

A ne Invariant Gradient Flows

An aane invariant metric allowing one to compute aane invariant gradient descent ows is rst presented in this work. This means that given an aane invariant energy, we compute based on this metric the ow that minimizes this energy as fast as possible and in an aane invariant way. Two examples are then presented. The rst one shows that the aane ow minimizing the area enclosed by a planar curve is...