Orbit Growth Of Contact Structures After Surgery
Dynamical Systems
2019-11-01 v1 Symplectic Geometry
Abstract
Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not topologically orbit-equivalent to any algebraic flow, including examples on many hyperbolic 3-manifolds, and we show how the surgery produces dynamical complexity for any Reeb flow compatible with the resulting contact structure. This includes exponential complexity when neither the surg-ered flow nor the surgered manifold are hyperbolic. We also demonstrate the use in dynamics of contact homology, a powerful tool in contact geometry.
Keywords
Cite
@article{arxiv.1910.14357,
title = {Orbit Growth Of Contact Structures After Surgery},
author = {Patrick Foulon and Boris Hasselblatt and Anne Vaugon},
journal= {arXiv preprint arXiv:1910.14357},
year = {2019}
}