Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.展开更多
基金Project supported by NSF (10171034) of ChinaNSF (970395) of Guangdong province
文摘Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.
