Non-hyperbolic minimal sets for tridiagonal competitive-cooperative systems

Fang, Chun; Gyllenberg, Mats; Wang, Yi

doi:10.1090/S0002-9939-2015-12536-1

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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