Weak mixing implies mixing for maps on topological graphs

Abstract

In section 1, we correct an error in the proof of Lemma 3.1 in L. Alsedà, M.A. del Río, and J.A. Rodríguez. Transitivity and dense periodicity for graph maps. J. Difference Equ. Appl. 9, 577–598, 2003. In section 2 we give a simple proof that weak mixing implies mixing for maps on topological graphs. The proofs can also be extended to (not necessarily compact) intervals, so in particular, this paper shows that for one-dimensional manifolds, weak mixing implies mixing.

Keywords:

• Maps on topological graphs
• Topologically mixing
• Topologically weakly mixing
• One-dimensional manifolds
• Primary 37E25
• 37B20
• Secondary 37E05
• 37E10