Universität zu Köln

Albers, Peter, Geiges, Hansjoerg and Zehmisch, Kai ORCID: 0000-0002-9512-860X (2018). Reeb dynamics inspired by Katok's example in Finsler geometry. Math. Ann., 370 (3-4). S. 1883 - 1908. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1807

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Abstract

Inspired by Katok's examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result is concerned with a contact-geometric description of magnetic flows on the 2-sphere found recently by Benedetti. We give a simple interpretation of that work in terms of a quaternionic symmetry. In the second part, we use Hamiltonian circle actions on symplectic manifolds to produce compact, connected contact manifolds in dimension at least five with arbitrarily large numbers of periodic Reeb orbits. This contrasts sharply with recent work by Cristofaro-Gardiner, Hutchings and Pomerleano on Reeb flows in dimension three. With the help of Hamiltonian plugs and a surgery construction due to Laudenbach we reprove a result of Cieliebak: one can produce Hamiltonian flows in dimension at least five with any number of periodic orbits; in dimension three, with any number greater than one.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Albers, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED Geiges, Hansjoerg UNSPECIFIED UNSPECIFIED UNSPECIFIED Zehmisch, Kai UNSPECIFIED orcid.org/0000-0002-9512-860X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-192215
DOI:	10.1007/s00208-017-1612-5
Journal or Publication Title:	Math. Ann.
Volume:	370
Number:	3-4
Page Range:	S. 1883 - 1908
Date:	2018
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1807
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CONTACT; ORBIT Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19221