One property of components of a chain recurrent set (Q2516365)

Chain recurrent sets, introduced by \textit{C. Conley} [Ergodic Theory Dyn. Syst. 8, 11--26 (1988; Zbl 0687.58033)] are part of the fundamental decomposition of topological dynamical systems into gradient-like and chain recurrent parts. Here it is shown that on a compact manifold the connectivity components of a chain recurrent set must satisfy the stronger property of pointed \(1\)-movability. In particular, this shows that certain solenoids cannot arise as a component of a chain recurrent set despite occurring as a minimal set of a flow.