Dynamical properties of monotone dendrite maps

作者：Naghmouchi Issam^*

来源：Topology and Its Applications, 2012, 159(1): 144-152.

DOI：10.1016/j.topol.2011.08.020

• Dendrite map
• omega-Limit set
• Minimal set
• Periodic point
• Transitive
• Li-Yorke pair
• Pointwise recurrent

We show that for a monotone dendrite map f : D -> D, any omega-limit set is either finite or a minimal Cantor set. We also prove that UR(f) = R(f) = A(f) = <(P(f))over bar> where P(f), UR(f), R(f) and A(f) denote the sets of periodic points, uniformly recurrent points, recurrent points and the union of all omega-limit sets respectively. Moreover, we prove that the following properties are equivalent: (i) R(f) = D, (ii) <(R(f))over bar> = D and (iii) D\End(D) subset of P(f).

• 出版日期2012-1-1