70 citations · 316 across the 56 of their papers we have counts for
5 papers · 1 filter
Contact topology and hydrodynamics II: solid tori
John Etnyre, Robert Ghrist
We prove the existence of periodic orbits for steady Euler flows on all Riemannian solid tori. By using the correspondence theorem from part I of this series, we reduce the p…
Contact topology and hydrodynamics III: knotted flowlines
John Etnyre, Robert Ghrist
We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Rie…
Configuration spaces and braid groups on graphs in robotics
Robert Ghrist
Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial setti…
Stratified integrals and unknots in invisid flows
John B. Etnyre, Robert W. Ghrist
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an ex…
Gradient flows within plane fields
John Etnyre, Robert Ghrist
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such…