Cyclic Approximation to K-Stasis

TL;DR

This paper demonstrates that near a point where a linear combination of k smooth vector fields vanishes, small cycles can typically be formed from segments of each flow, addressing a previously open question.

Contribution

It provides a generic construction of small cycles near points where a linear combination of vector fields is zero, answering an open problem in the field.

Findings

Existence of small cycles near points where linear combinations vanish

Generic conditions for cycle formation from flow segments

Resolution of a question posed in arXiv:math/0504365

Abstract

If a linear combination of k smooth vector fields is zero at a point, then, generically, near this point there are small cycles comprised of segments from the flow of each vector field. This answers a question posed in arXiv:math/0504365.