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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Homoclinic intersections and indecomposability


Author: Marcy Barge
Journal: Proc. Amer. Math. Soc. 101 (1987), 541-544
MSC: Primary 58F15; Secondary 54F20, 54H20
DOI: https://doi.org/10.1090/S0002-9939-1987-0908665-6
MathSciNet review: 908665
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Abstract: The closure of a one-dimensional unstable manifold of a hyperbolic fixed point of a diffeomorphism having homoclinic points is, under mild assumptions, shown to be an indecomposable continuum. As a result, dynamical systems possessing such behavior cannot be modeled using inverse limits based on any simple space.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908665-6
Keywords: Homoclinic point, inverse limit, indecomposable continuum
Article copyright: © Copyright 1987 American Mathematical Society