NON-HYPERBOLIC MINIMAL SETS FOR TRIDIAGONAL COMPETITIVE-COOPERATIVE SYSTEMS

摘要

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 R-1 x 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 R-1 x H(f). We further propose a conjecture in the case that the dimension of the center-space is greater than one.