INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS IH, SU-ION;
Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let and let be the set of the images of under especially all Chebyshev morphisms. Then for any , we show that there are only a finite number of elements in which are S-integral on relative to (). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on , which generalizes the above finiteness result for Chebyshev morphisms.