Topological horseshoes
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- by Judy Kennedy and James A. Yorke
- Trans. Amer. Math. Soc. 353 (2001), 2513-2530
- DOI: https://doi.org/10.1090/S0002-9947-01-02586-7
- Published electronically: February 15, 2001
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Abstract:
When does a continuous map have chaotic dynamics in a set $Q$? More specifically, when does it factor over a shift on $M$ symbols? This paper is an attempt to clarify some of the issues when there is no hyperbolicity assumed. We find that the key is to define a “crossing number” for that set $Q$. If that number is $M$ and $M>1$, then $Q$ contains a compact invariant set which factors over a shift on $M$ symbols.References
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Bibliographic Information
- Judy Kennedy
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Email: jkennedy@math.udel.edu
- James A. Yorke
- Affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
- Email: yorke@ipst.umd.edu
- Received by editor(s): March 16, 1998
- Received by editor(s) in revised form: December 21, 1998
- Published electronically: February 15, 2001
- Additional Notes: This research was supported by the National Science Foundation, Division of Mathematical Sciences
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2513-2530
- MSC (1991): Primary 58F12, 54F20; Secondary 54F50, 58F20
- DOI: https://doi.org/10.1090/S0002-9947-01-02586-7
- MathSciNet review: 1707195