Homoclinic intersections and indecomposability
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- by Marcy Barge PDF
- Proc. Amer. Math. Soc. 101 (1987), 541-544 Request permission
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.References
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- R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473–487. MR 217808, DOI 10.1016/0040-9383(67)90005-5
Additional Information
- © Copyright 1987 American Mathematical Society
- 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