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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.

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One-dimensional contracting singular horseshoe
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by D. Carrasco-Olivera, C. A. Morales and B. San Martín PDF
Proc. Amer. Math. Soc. 138 (2010), 4009-4023 Request permission

Abstract:

In this paper we prove some kind of structural stability defined as usual but restricted to a certain subset of one-dimensional maps coming from first return maps associated to singular cycles for vector fields in manifolds with boundary. The motivation is the stability of the Singular Horseshoes introduced by Labarca and Pacifico where an expanding condition on the singularity holds. Here we obtain analogous result but under a contracting condition.
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  • D. Carrasco-Olivera
  • Affiliation: Departamento de Matemática, Facultad de Ciencias, Universidad del Bío Bío, Av. Collao #1202, Casilla 5-C, Región de Concepción, Chile
  • Email: dcarrasc@ubiobio.cl
  • C. A. Morales
  • Affiliation: Instituto de Matemáticas, Universidad Federal de Rio de Janeiro, P.O. Box 68530, 21945-970, Rio de Janeiro, Brasil
  • MR Author ID: 611238
  • ORCID: 0000-0002-4808-6902
  • Email: morales@impa.br
  • B. San Martín
  • Affiliation: Departamento de Matematicas, Universidad Católica del Norte, Av. Angamos 0610, Casilla 1280, Antofagasta, Chile
  • Email: sanmarti@ucn.cl
  • Received by editor(s): June 11, 2009
  • Received by editor(s) in revised form: November 26, 2009, January 13, 2010, and January 18, 2010
  • Published electronically: June 16, 2010
  • Additional Notes: The first author was supported in part by Project Mecesup 0202-UCN; Project Fondecyt No. 1040682; Project ADI 17 Anillo en Sistemas Dinámicos de Baja Dimensión, Chile; CONICYT Proyecto Inserción de Nuevos Invertigadores en la Academia, 2009, Folio 79090039.
    The second author was partially supported by CNPq, FAPERJ and PRONEX-Brazil.
    The third author was partially supported by Project Fondecyt No. 1040682 and Project ADI 17, Anillo en Sistemas Dinámicos de Baja Dimensión, CONICYT - Chile and PRONEX-Brazil.
  • Communicated by: Bryna Kra
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 4009-4023
  • MSC (2010): Primary 37E05, 37D25; Secondary 37D30, 37F15
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10392-1
  • MathSciNet review: 2679622