Small periodic homeomorphisms of chainable continua (Q1200690)

It is known from a paper by \textit{J. A. Toledo} [Can. J. Math. 38, 563-575 (1986; Zbl 0604.54031)] that the pseudo-arc admits for arbitrary \(n\) arbitrarily small homeomorphisms of period \(n\). The author shows that there are other chainable continua having this property, e.g. a continuum which is the wedge of the pseudo-arc or the closed interval of reals. Consider namely the pseudo-arc sticked with the interval at the point \(a\). The author shows that if a positive integer \(n\) and a positive \(\varepsilon\) are given, then there exists a homeomorphism of period \(n\) on the pseudo-arc moving points no more than \(\varepsilon\) and leaving the point fixed. Joining this homeomorphism with the identity on the interval a homeomorphism is obtained leading to the desired result. The problem arises about the existence of arbitrarily small periodic homeomorphisms on indecomposable chainable continua other than the pseudo-arc.