Attracting sets on surfaces
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- by J. Iglesias, A. Portela, A. Rovella and J. Xavier PDF
- Proc. Amer. Math. Soc. 143 (2015), 765-779 Request permission
Abstract:
Let $f$ be a continuous endomorphism of a surface $M$, and $A$ an attracting set such that the restriction $f|_A: A \to A$ is a $d:1$ covering map. We show that if $f$ is a local homeomorphism, then $f$ is also a $d:1$ covering of the immediate basin of $A$. Moreover, the techniques provide a characterization of invariant $d:1$ continua on surfaces. These results are no longer true on manifolds of dimensions at least three.References
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Additional Information
- J. Iglesias
- Affiliation: Facultad de Ingenieria, Universidad de La República, IMERL, Julio Herrera y Reissig 565, C. P. 11300, Montevideo, Uruguay
- Email: jorgei@fing.edu.uy
- A. Portela
- Affiliation: Facultad de Ingenieria, Universidad de La República, IMERL, Julio Herrera y Reissig 565, C. P. 11300, Montevideo, Uruguay
- Email: aldo@fing.edu.uy
- A. Rovella
- Affiliation: Facultad de Ciencias, Universidad de La República, Centro de Matemática, Iguá 4225, C. P. 11400, Montevideo, Uruguay
- Email: leva@cmat.edu.uy
- J. Xavier
- Affiliation: Facultad de Ingenieria, Universidad de La República, IMERL, Julio Herrera y Reissig 565, C. P. 11300, Montevideo, Uruguay
- Email: jxavier@fing.edu.uy
- Received by editor(s): August 3, 2012
- Received by editor(s) in revised form: March 13, 2013, May 3, 2013, May 7, 2013, May 20, 2013, May 22, 2013, and May 27, 2013
- Published electronically: October 16, 2014
- Communicated by: Nimish Shah
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 765-779
- MSC (2010): Primary 37C70; Secondary 37B25
- DOI: https://doi.org/10.1090/S0002-9939-2014-12274-X
- MathSciNet review: 3283663