Collapsed indecomposable continua in area preserving two-dimensional dynamical systems
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- by Judy Kennedy PDF
- Proc. Amer. Math. Soc. 135 (2007), 2073-2080 Request permission
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 $W^{u+}(p)$.References
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Additional Information
- Judy Kennedy
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Email: jkennedy@math.udel.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2073-2080
- MSC (2000): Primary 37C29, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-07-08751-5
- MathSciNet review: 2299483