التفاصيل البيبلوغرافية
| العنوان: |
Genus zero global surfaces of section for Reeb flows and a result of Birkhoff. |
| المؤلفون: |
Hryniewicz, Umberto L., Salomão, Pedro A. S., Wysocki, Krzysztof |
| المصدر: |
Journal of the European Mathematical Society (EMS Publishing); 2023, Vol. 25 Issue 9, p3365-3451, 87p |
| مصطلحات موضوعية: |
BIRKHOFF'S theorem (Relativity), COMBINATORIAL dynamics, EXISTENCE theorems, SET theory, GENERALIZATION |
| مستخلص: |
We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed 3-manifold to bound a positive global surface of section with genus zero. These conditions turn out to be C8-generically necessary. Moreover, they involve linking assumptions on periodic orbits with Conley-Zehnder index ranging in a finite set determined by the ambient contact geometry. As an application, we reprove and generalize a classical result of Birkhoff on the existence of annulus-like global surfaces of section for geodesic flows on positively curved two-spheres. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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