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Non-hyperbolic minimal sets for tridiagonal competitive-cooperative systems


Authors: Chun Fang, Mats Gyllenberg and Yi Wang
Journal: Proc. Amer. Math. Soc. 143 (2015), 3063-3074
MSC (2010): Primary 37B55, 34C27
DOI: https://doi.org/10.1090/S0002-9939-2015-12536-1
Published electronically: February 26, 2015
MathSciNet review: 3336631
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Abstract: The dynamics on non-hyperbolic minimal sets is investigated for non-linear competitive-cooperative tridiagonal systems in time-recurrent structures including almost periodicity and almost automorphy. With the help of exponential separation of the Floquet bundles proved in a previous work of the present authors, we prove that the skew-product flow on a minimal set $ Y$ is topologically conjugate to a minimal flow in $ \mathbb{R}^1\times H(f)$ (where $ H(f)$ is the hull of $ f$), provided that the center-space associated with $ Y$ is one-dimensional. In particular, if $ Y$ is uniquely ergodic, then $ Y$ can be embedded into $ \mathbb{R}^1\times H(f)$. We further propose a conjecture in the case that the dimension of the center-space is greater than one.


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Additional Information

Chun Fang
Affiliation: Department of Mathematics and Statistics, University of Helsinki, FIN-00014, Finland
Email: chun.fang@helsinki.fi

Mats Gyllenberg
Affiliation: Department of Mathematics and Statistics, University of Helsinki, FIN-00014, Finland
Email: mats.gyllenberg@helsinki.fi

Yi Wang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Address at time of publication: Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China.
Email: wangyi@ustc.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12536-1
Received by editor(s): November 3, 2013
Received by editor(s) in revised form: March 25, 2014, and March 28, 2014
Published electronically: February 26, 2015
Additional Notes: The third author was partially supported by NSF of China No. 91130016, 11371338, and the Finnish Center of Excellence in Analysis and Dynamics.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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