The Research Of Pseudo Orbit Tracing Property Of Continuous Maps On The Y Space

In recent years,many scholars have studied dynamics generated by tree maps,for example,the turbulence,the characteristics of the ?-limit set,the topological transitiveness and the topological mixing,the set of chain equiv-alent points and the turbulence,the attractive center and the topological en-tropy,and so on.The tree(i.e.,the tree is the one dimension compact connect-ed branch manifold which doesn't contain circle)which is homeomorphic to the set of X3={z?C:z3 ?[[,1]} is called Y-stars,which is denoted by Y.In this thesis,it is mainly researched the pseudo orbit tracing property of the mapping on the Y space,the inverse pseudo orbit tracing property of the mapping on the Y space,and the relationship between pseudo orbit tracing property and pointwise chain recurrence of the mapping on the Y space.In the third Chapter,let f:Y?Y be a continuous map,P(f)=F(f)=,and let F(f)be nowhere dense.the following conditions have been proved to be equivalent:(1)f has the pseudo orbit tracing property;(2)if for some x?Y,fn(x)converges to a fixed point p,and there exists a nontrapping neighborhood[p,q]of p,then for each neighborhood Ox of x,and arbitrary point z ?[p,q),there exists n ? N,such that[p,z](?)fn(Ox).In the fourth Chapter,let f:Y ? Y be a homeomorphism,P(f)=F(f)and let F(f)be nowhere dense.The following conditions have been proved to be equivalent:(1)f has the pseudo orbit tracing property;(2)f has positive Tc-inverse pseudo orbit tracing property;(3)f has positive Th-inverse pseudo orbit tracing property.In addition,we also have got several equivalent conditions of inverse pseudo orbit tracing property of the self-homeomorphism of the interval.In the fifth Chapter,let f:Y?Y be a continuous map.It has been proved that if f is pointwise chain recurrent,then f hasn't the pseudo orbit tracing property.