Arcs, balls and spheres that cannot be attractors in $\mathbb {R}^3$
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- by J. J. Sánchez-Gabites PDF
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Abstract:
For any compact set $K \subseteq \mathbb {R}^3$ we define a number $r(K)$ that is either a nonnegative integer or $\infty$. Intuitively, $r(K)$ provides some information on how wildly $K$ sits in $\mathbb {R}^3$. We show that attractors for discrete or continuous dynamical systems have finite $r$ and then prove that certain arcs, balls and spheres cannot be attractors by showing that their $r$ is infinite.References
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Additional Information
- J. J. Sánchez-Gabites
- Affiliation: Facultad de Ciencias Económicas y Empresariales, Universidad Autónoma de Madrid, Campus Universitario de Cantoblanco, 28049 Madrid, España
- Email: JaimeJ.Sanchez@uam.es
- Received by editor(s): June 20, 2013
- Received by editor(s) in revised form: May 14, 2014
- Published electronically: June 24, 2015
- Additional Notes: The author was partially supported by MICINN (grant MTM 2009-07030).
The author wishes to express his deepest gratitude to Professor Rafael Ortega (Universidad de Granada) for his generous support and encouragement during the writing of this paper - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3591-3627
- MSC (2010): Primary 54H20, 37B25, 37E99
- DOI: https://doi.org/10.1090/tran/6570
- MathSciNet review: 3451887