Compact invariant sets do not imply periodic orbits - examples of geodesic, Reeb and Hamiltonian flows

Symplectic geometry and topology

19 November 14:00 - 15:00

Nena-Maria Röttgen - Westfälische Wilhelms-Universität Münster

Examples of non vanishing vector fields on closed manifolds without periodic orbits are mainly constructed by using Wilson plugs. I will introduce the definition of a plug and explain how it can be used to find examples of such vector fields. For Reeb flows plugs can not exist but I will present examples of semi contact plugs in dimension five and higher, compare their dynamics with the 3-dimensional situation, show similar results for the geodesic flow and discuss relations to the Weinstein conjecture. Finally I will apply the semi contact plug construction to build Hamiltonian plugs.
Tobias Ekholm,
Uppsala University
Yakov Eliashberg
Stanford University
Lenhard Ng
Duke University
Ivan Smith
University of Cambridge


Tobias Ekholm


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