## Non-hyperbolic minimal sets for tridiagonal competitive-cooperative systems

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- by Chun Fang, Mats Gyllenberg and Yi Wang PDF
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**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.## References

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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