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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

One-dimensional contracting singular horseshoe


Authors: D. Carrasco-Olivera, C. A. Morales and B. San Martín
Journal: Proc. Amer. Math. Soc. 138 (2010), 4009-4023
MSC (2010): Primary 37E05, 37D25; Secondary 37D30, 37F15
Published electronically: June 16, 2010
MathSciNet review: 2679622
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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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Additional Information

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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10392-1
PII: S 0002-9939(2010)10392-1
Keywords: One-dimensional maps, conjugation, symbolic dynamic, nonwandering set, transitive set
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
Article copyright: © Copyright 2010 American Mathematical Society