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Conference «Hyperbolic Dynamics and Structural Stability» Dedicated to the 85th Anniversary of D. V. Anosov
November 12, 2021 18:00–18:45, Moscow, online
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Surgered contact flows, hyperbolicity, and orbit growth
Boris Hasselblatt Tufts University
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Abstract:
This is a joint project with P. Foulon and A. Vaugon.
- Foulon–Dingâ–Geiges–Weinstein–Handel–Thurston surgery is a contact surgery on the unit tangent bundle of a surface.
- This forces orbit complexity.
- It produces several contact 3-flows.
- From the fiber flow a flow with quadratic or exponential complexity.
- From the geodesic flow a contact structure whose every Reeb flow has positive entropy.
- If the surgered geodesic flow is hyperbolic, then it has increased orbit growth.
- There are 3-manifolds with two contact flows, one exponentially complex, one polynomially.
Language: English
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