Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Attracting sets on surfaces
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37C70, 37B25
  • Retrieve articles in all journals with MSC (2010): 37C70, 37B25
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