Graph maps with zero topological entropy and sequence entropy pairs

Abstract

A. We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal -limit set), and a non-diagonal pair is an NS-pair if and only if it is an IN-pair if and only if it is an IT-pair. This completes characterization of zero topological sequence entropy for graph maps.

Topological sequence entropy and topological dynamics of tree maps

“…• Given A 1 , A 2 , ..., A k ⊂ X, we say that I ⊂ N is an independence set of A 1 , A 2 , ..., A k if for any non-empty finite subset J ⊂ I with m elements and any s 1 , ..., s m ∈ {1, 2, ..., k} we have that ∩ j∈J f −j (A s j ) = ∅. Following [21], a pair (x, y) ∈ X × X is called a IN-pair if for any neighborhoods U, V of x, y, respectively, the pair {U, V } has arbitrarily large finite independence set for the product map…”