ABSTRACT

Corresponding to a given sequence of natural numbers N= (ni, n^, ...) with HJ > 2 for each j there is the solenoid Sjv, the inverse limit

,...,exp

A character of EAT is a continuous homomorphism x '• ^ N —» S11 C C. Any continuous map EJV —> C may be uniformly approximated by linear combinations of finitely many characters of EAT, see, e.g., [P],[Wa]. Thus for x € ETV the induced map Ax : R —> R, 1i-> 5o (a; + TTJV (£)) is a limit periodic function, meaning that it can be uniformly approximated to within any prescribed £ > 0 by a periodic function (depending on e). In our case we may use trigonometirc polynomials with rational periods for these approximations, (see, e.g., [C2]). In what follows we will use the map S to describe the dynamics of /.