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A robustly chain transitive attractor with singularities of different indices

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  01 June 2012

Christian Bonatti ,
Ming Li  and
Dawei Yang
Christian Bonatti
Affiliation:
Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon 21004, France (bonatti@u-bourgogne.fr)
Ming Li
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China (limingmath@nankai.edu.cn)
Dawei Yang
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, PR China (yangdw1981@gmail.com)
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Abstract

Given a 4-manifold, we build a non-empty ${C}^{1} $-open set of vector fields having a (chain transitive) attractor containing singularities of different indices. Then, we begin the study of the hyperbolic properties of such a robust singular attractor.

Keywords

singular attractorrobustly chain transitivepartially hyperbolicindex

MSC classification

Secondary: 37D30: Partially hyperbolic systems and dominated splittings
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 3 , July 2013 , pp. 449 - 501
Copyright
©Cambridge University Press 2012 

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