TY - GEN

T1 - Integral Curves of a Vector Field with a Fractal Discontinuity

AU - Jeffrey, Mike

AU - Hahn, J.

PY - 2017/5/27

Y1 - 2017/5/27

N2 - Nonsmooth systems are typically studied with smooth or piecewise-smooth boundaries between smooth vector fields, especially with linear or hyper-planar boundaries. What happens when there is a boundary that is not as simple, for example a fractal? Can a solution to such a system slide or “chatter” along this boundary? It turns out that the dynamics is rather fascinating, and yet contained within A.F. Filippov’s theory (as promised in Utkin, Comments for the continuation method by A.F. Filippov for discontinuous systems, parts I and II, [2] from this volume).

AB - Nonsmooth systems are typically studied with smooth or piecewise-smooth boundaries between smooth vector fields, especially with linear or hyper-planar boundaries. What happens when there is a boundary that is not as simple, for example a fractal? Can a solution to such a system slide or “chatter” along this boundary? It turns out that the dynamics is rather fascinating, and yet contained within A.F. Filippov’s theory (as promised in Utkin, Comments for the continuation method by A.F. Filippov for discontinuous systems, parts I and II, [2] from this volume).

U2 - 10.1007/978-3-319-55642-0_17

DO - 10.1007/978-3-319-55642-0_17

M3 - Conference Contribution (Conference Proceeding)

SN - 9783319556413

T3 - Trends in Mathematics

SP - 95

EP - 99

BT - Extended Abstracts Spring 2016

PB - Birkhäuser Basel

ER -