Stability of Periodic Orbits and Return Trajectories of Continuous Multi-valued Maps on Intervals  

作　　者：Tai Xiang SUN Fan Ping ZENG Guang Wang SU Bin QIN 

机构地区：[1]Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics

出　　处：《Acta Mathematica Sinica,English Series》2018年第7期1121-1130,共10页数学学报（英文版）

基　　金：Supported by NNSF of China(Grant No.11761011);NSF of Guangxi(Grant Nos.2016GXNSFBA380235and 2016GXNSFAA380286);YMTBAPP of Guangxi Colleges(Grant No.2017KY0598);SF of Guangxi Univresity of Finance and Economics(Grant No.2017QNA04)

摘　　要：Let I be a compact interval of real axis R, and （L, H） be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f ： I →L be a continuous multi-valued map. Assume that Pn = （x0, x1,..., xn） is a return trajectory of f and that p ∈ [min Pn, max Pn] with p ∈ f（p）. In this paper, we show that if there exist k （≥ 1） centripetal point pairs of f （relative to p） in {（xi;xi＋l） ： 0 ≤ i ≤ n- 1} and n =sk＋r （0 ≤ r ≤ k - 1）, then f has an R-periodic orbit, where R=s＋1 ifsiseven, and R =s if s is odd and r = 0, and R=s＋2 if s is odd and r 〉0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to L.Let I be a compact interval of real axis R, and （L, H） be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f ： I →L be a continuous multi-valued map. Assume that Pn = （x0, x1,..., xn） is a return trajectory of f and that p ∈ [min Pn, max Pn] with p ∈ f（p）. In this paper, we show that if there exist k （≥ 1） centripetal point pairs of f （relative to p） in {（xi;xi＋l） ： 0 ≤ i ≤ n- 1} and n =sk＋r （0 ≤ r ≤ k - 1）, then f has an R-periodic orbit, where R=s＋1 ifsiseven, and R =s if s is odd and r = 0, and R=s＋2 if s is odd and r 〉0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to L.

关 键 词：Continuous multi-valued map periodic orbit STABILITY 

分 类 号：O177[理学—数学]