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# Gradient flows within plane fields

@inproceedings{Etnyre1999GradientFW, title={Gradient flows within plane fields}, author={John B. Etnyre and Robert Ghrist}, year={1999} }

- Published 1999
DOI:10.1007/s000140050102

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 vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple (i.e., a graph-manifold). Furthermore, there are strong restrictions on the types of gradient flows realized within plane fields: such flows lie on the boundary of the space of nonsingular… CONTINUE READING