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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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Non-hyperbolic minimal sets for tridiagonal competitive-cooperative systems
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by Chun Fang, Mats Gyllenberg and Yi Wang PDF
Proc. Amer. Math. Soc. 143 (2015), 3063-3074 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • 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
  • MathSciNet review: 3336631