Intra-orbit separation of orbits of tree maps.

In this paper, we will generalize the notion of separation index, which was introduced by G. Manjunath et al (2006), to tree maps, and use the notion to characterize the intra-orbit. separation for the orbits of continuous transitive maps on a tree. For a. transitive map f, we will show: (i) if the separation index γ of f is positive, then for every 0 < τ < 7γ, (xs,xt) is a Li-Yorke pair of modulus τ, where xs and Xt be any two distinct points on a dense orbit; (ii) there is a natural number n such that the separation index of fn is greater than zero. [ABSTRACT FROM AUTHOR]