Mixed Maps for Kolmogoroff-Nagumo-Type Averaging on the Compact Stiefel Manifold

A low complexity Lie group method on the Stiefel manifold

A low complexity Lie group method for numerical integration of ordinary differential equations on the orthogonal Stiefel manifold is presented. Based on the quotient space representation of the Stiefel manifold we provide a representation of the tangent space suitable for Lie group methods. According to this representation a special type of generalized polar coordinates (GPC) is defined and use...

Statistics on the (compact) Stiefel manifold: Theory and Applications

A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spaces and performed statistical analysis of data ...

On the Classification of Transitive Effective Actions on Stiefel Manifolds

Introduction. Let G be a compact connected Lie group and H a closed subgroup of G. Then the coset space G/H is a smooth manifold with G acting transitively as translations. It is easy to see that the natural action of G on G/H is effective if and only if H contains no nontrivial normal subgroup of G. For a given compact homogeneous space M=G/H, one might ask whether there are any other (differe...

On images of continuous functions from a compact manifold to Euclidean space

Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system.

We investigate the organization of mixed-mode oscillations in the self-coupled FitzHugh-Nagumo system. These types of oscillations can be explained as a combination of relaxation oscillations and small-amplitude oscillations controlled by canard solutions that are associated with a folded singularity on a critical manifold. The self-coupled FitzHugh-Nagumo system has a cubic critical manifold f...