Invariant theory and reversible-equivariant vector fields

Bifurcation and branching of equilibria in reversible equivariant vector fields

We study steady-state bifurcation in reversible equivariant vector fields. We assume an action on the phase space of a compact Lie group G with a normal subgroup H of index two, and study vector fields that are H-equivariant and have all elements of the complement G \ H as time-reversal symmetries. We focus on separable bifurcation problems that can be reduced to equivariant steady-state bifurc...

Homology of Equivariant Vector Fields

Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X . We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the quotient X/K.

Gröbner Bases, Invariant Theory and Equivariant Dynamics

This paper is about algorithmic invariant theory as it is required within equivariant dynamical systems. The question of generic bifurcation equations (arbitrary equivariant polynomial vector) requires the knowledge of fundamental invariants and equivariants. We discuss computations which are related to this for finite groups and semi-simple Lie groups. We consider questions such as the complet...

Modeling of ‎I‎nfinite Divisible Distributions Using Invariant and Equivariant Functions

‎Basu’s theorem is one of the most elegant results of classical statistics‎. ‎Succinctly put‎, ‎the theorem says‎: ‎if T is a complete sufficient statistic for a family of probability measures‎, ‎and V is an ancillary statistic‎, ‎then T and V are independent‎. ‎A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics‎. ‎In addition ...

Admissible vector fields and quasi-invariant measures∗