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Article
Topological Contact Dynamics II: Topological Automorphisms, Contact Homeomorphisms, and Non-Smooth Contact Dynamical Systems
Transactions of the American Mathematical Society (2014)
  • Stefan Müller, University of Illinois at Urbana-Champaign
  • Peter Spaeth, Penn State University
Abstract
This sequel to our previous paper continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact structure and a contact form are the appropriate transformation groups of contact dynamical systems. This article includes an examination of the groups of time-one maps of topological contact and strictly contact isotopies, and the construction of a bi-invariant metric on the latter. Moreover, every topological contact or strictly contact dynamical system is arbitrarily close to a continuous contact or strictly contact dynamical system with the same end point. In particular, the above groups of time-one maps are independent of the choice of norm in the definition of the contact distance. On every contact manifold we construct topological contact dynamical systems with time-one maps that fail to be Lipschitz continuous, and smooth contact vector fields whose flows are topologically conjugate but not conjugated by a contact -diffeomorphism.
Keywords
  • Contact metric,
  • Contact topology,
  • Hamiltonian function,
  • Conformal factor,
  • Transformation law,
  • Topological group,
  • Left invariant metric
Disciplines
Publication Date
September, 2014
DOI
10.1090/S0002-9947-2013-06123-5
Publisher Statement
This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Transactions of the American Mathematical Society.
Citation Information
Stefan Müller and Peter Spaeth. "Topological Contact Dynamics II: Topological Automorphisms, Contact Homeomorphisms, and Non-Smooth Contact Dynamical Systems" Transactions of the American Mathematical Society Vol. 366 Iss. 9 (2014) p. 5009 - 5041 ISSN: 1088-6850
Available at: http://works.bepress.com/stefan-muller/4/