Canonical symbolic dynamics for one-dimensional generalized solenoids (Q2716159)

Canonical shift of finite type covers of one-dimensional generalized solenoids are constructed in the following sense. Given as input a one-solenoid \(X\) in the sense of \textit{R. F. Williams} [Global analysis, Proc. Sympos. Pure Math. 14, 341-361 (1970; Zbl 0213.50401)] with shift map \(f\), and a union \(O\) of finitely many periodic orbits of \(f\). The procedure produces a mixing shift of finite type \(\Sigma(X,f,O)\) and a continuous surjection \(\pi(X,f,O)\) from the shift to the solenoid intertwining the shift maps. A conjugacy of one-solenoids sending \((X_1,f_1,O_1)\) to \((X_2,f_2,O_2)\) lifts uniquely to a conjugacy of the covering shifts of finite type. This construction is exploited to find nontrivial and readily computable invariants that distinguish between closely-related one-solenoids.