Skip Navigation



Journal of Topology Advance Access published online on October 25, 2007
Journal of Topology, doi:10.1112/jtopol/jtm005
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
1/1/115    most recent
jtm005v1
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Burghelea, D.
Right arrow Articles by Haller, S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

Dynamics, Laplace transform and spectral geometry

Dan Burghelea

Department of Mathematics, The Ohio State University, 231 West Avenue, Columbus, OH 43210, USA burghele{at}math.ohio-state.edu

Stefan Haller

Department of Mathematics, University of Vienna, Nordbergstraße 15, A-1090, Vienna, Austria stefan.haller{at}univie.ac.at


  Abstract

In this paper, we consider vector fields on a closed manifold whose instantons and closed trajectories can be ‘counted’. Vector fields which admit Lyapunov closed one forms belong to this class. We show that under an additional hypothesis, ‘the exponential growth property’, the counting functions of instantons and closed trajectories have Laplace transforms which can be related to the topology and the geometry of the underlying manifold. The purpose of this paper is to introduce and explore the concept ‘exponential growth property’, and to describe these Laplace transforms.

Received February 24, 2007.

2000 Mathematics Subject Classification 57R20, 57R58, 57R70, 57Q10, 58J52

Part of this work was done while the second author enjoyed the warm hospitality of the Ohio State University. The second author was partially supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austrian Science Fund), project number P14195-MAT. Part of this work was carried out when the first author enjoyed the hospitality of IHES in Bures sur Yvette and the second author had the pleasure of visiting the Max Planck Institute for Mathematics in Bonn.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.