Constructing Birkhoff sections for pseudo-Anosov flows with controlled complexity
arXiv:2206.09586 · doi:10.1017/etds.2023.105
Abstract
We introduce a new method of constructing Birkhoff sections for pseudo-Anosov flows, which uses the connection between pseudo-Anosov flows and veering triangulations. This method allows for explicit constructions, as well as control over the Birkhoff section in terms of its Euler characteristic and the complexity of the boundary orbits. In particular, we show that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.
arXiv commentv2 - 56 pages, 30 figures; introduction rewritten and other minor changes, to appear in Ergodic Theory and Dynamical Systems
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