Unknotted periodic orbits for Reeb flows on the three-sphere
Słowa kluczowe
Reeb flows, unknotted periodic orbits, three-sphere, theory for PDE of Cauchy-Riemann typeAbstrakt
It is well known that a Reeb vector field on $S^3$ has a periodic solution. Sharpening this result we shall show in this note that every Reeb vector field $X$ on $S^3$ has a periodic orbit which is unknotted and has self-linking number equal to $-1$. If the contact form $\lambda$ is non-degenerate, then there is even a periodic orbit $P$ which, in addition, has an index $\mu (P) \in \{2,3\}$, and which spans an embedded disc whose interior is transversal to $X$. The proofs are based on a theory for partial differential equations of Cauchy-Riemann type for maps from punctured Riemann surfaces into ${\mathbb R} \times S^3$, equipped with special almost complex structures related to the contact form $\lambda$ on $S^3$.Pobrania
Opublikowane
1996-06-01
Jak cytować
1.
HOFER, H., WYSOCKI, K. & ZEHNDER, E. Unknotted periodic orbits for Reeb flows on the three-sphere. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 1996, T. 7, nr 2, s. 219–244. [udostępniono 22.7.2024].
Numer
Dział
Articles
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0