熵与周期的关系

The Relations of Entropy and Period

设G为这样的有限图:它除含两个由一根线段连接的圈外不含其它圈,而且两个圈上的分支数相同.证明了连续自映射f∶G→G的熵为零当且仅当存在k≤[(Edg(G)+2End(G)+11)/2]个不同的奇数n1,n2,…,nk,使得Per(f)Uki=1U∞j=1ni2j,其中Edg(G)、End(G)分别表示G的边数、端点数.

Let GLet be a graph which contains no simple closed curve exact two circles which connected by a line. We prove that a continuous map f： G→G has zero topological entropy if and only if there exit at most k≤ [ （Edg（G） ＋2End（G） ＋ （f） 11 ）/21 different odd numbers n1 ,n2,…nk such that Per Per（f） belong to Ui=1^k uj=1^∞{n,2^f}.where Edg（G） is the number of edges of G. End（G）is the number of end points of （G）.