A map with topological minimal self-joinings in the sense of del Junco

Abstract

AbstractAndrés del Junco has proposed a definition of topological minimal self-joinings intended to parallel Dan Rudolph's measure-theoretic concept. By means of a rank-two ‘cutting and stacking’, this article constructs the first example of a system (a subshift) satisfying his proposed definition of 2-fold topological minimal self-joinings.The second part of the article shows that 2-fold topological minimal self-joinings does not imply 3-fold and that no map has 4-fold topological minimal self-joinings. This latter result follows from a generalization of a theorem of Schwartzman.