Dynamics of commuting homeomorphisms of chainable continua
Colloquium Mathematicum 121 (2010), 63-77 MSC: Primary 54H20; Secondary 37B40, 37B45. DOI: 10.4064/cm121-1-6
A chainable continuum, $X$, and homeomorphisms, $p,q:X\to X$, are constructed with the following properties:
(1) $p\circ q=q\circ p$,
(2) $p,q$ have simple dynamics,(3) $p\circ q$ is a positively continuum-wise fully expansive homeomorphism that has positive entropy and is chaotic in the sense of Devaney and in the sense of Li and Yorke.