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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Collapsed indecomposable continua in area preserving two-dimensional dynamical systems


Author: Judy Kennedy
Journal: Proc. Amer. Math. Soc. 135 (2007), 2073-2080
MSC (2000): Primary 37C29, 54H20
Published electronically: February 2, 2007
MathSciNet review: 2299483
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Abstract: While invariant indecomposable continua can occur in two dimensional area preserving dynamical systems, it is often the case that processes that would normally produce these continua instead produce a collapsed version of the continua because of the area preserving constraints. The collapsed continuum and the dynamics on it have a strong relationship to an indecomposable continuum in a related dynamical system. We also prove that the presence of a homoclinic point of a saddle point $ p$ in such a system has a branch $ W^{u+}(p)$ of its unstable manifold that is inaccessible from the complement of the closure of $ W^{u+}(p)$.


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Additional Information

Judy Kennedy
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: jkennedy@math.udel.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08751-5
PII: S 0002-9939(07)08751-5
Keywords: Homoclinic point, indecomposble continuum, area preserving, two dimensional.
Received by editor(s): March 3, 2006
Published electronically: February 2, 2007
Additional Notes: This research was supported by the National Science Foundation.
Communicated by: Michael Handel
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.