In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Petty, Taylor Michael, "Nonlocally Maximal Hyperbolic Sets for Flows" (2015). Theses and Dissertations. 5558.
dynamical systems, hyperbolic, locally maximal