Homoclinic intersections and indecomposability
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- by Marcy Barge
- Proc. Amer. Math. Soc. 101 (1987), 541-544
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908665-6
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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.References
- Marcy Barge, A method for constructing attractors, Ergodic Theory Dynam. Systems 8 (1988), no. 3, 331–349. MR 961734, DOI 10.1017/S0143385700004491
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473–487. MR 217808, DOI 10.1016/0040-9383(67)90005-5
Bibliographic 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