Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The minimal m ∈ NU {∞} such that Ωm(f) = Ωm+1(f) is called the depth of f. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2. Furthermore, we obtain some properties of non-wandering points of f.
Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of Mathematics,Shantou University,Shantou 515063,China
In this paper, we introduce the notion of the strongly simple cycles with some rotation pair for interval maps and prove that, if an interval map has a cycle with given rotation pair, then it, has a strongly simple cycle with the same rotation pair.
This paper considers the guaranteed cost control problem for a class of uncertain linear systems with both state and input delays. By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors, we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities. Two examples are presented which show the effectiveness of our approach.
