ALGEBRAIC INDEPENDENCE OF LOCAL CONJUGACIES AND RELATED QUESTIONS IN POLYNOMIAL DYNAMICS

摘要

Let K be an algebraically closed field of characteristic 0 and f is an element of K[t] a polynomial of degree d >= 2. There exists a local conjugacy psi(f) (t) is an element of tK[[1/t]] such that psi(f) (t(d)) = f(psi(f)(t)). It has been known that psi(f) is transcendental over K(t) if f is not conjugate to t(d) or a constant multiple of the Chebyshev polynomial. In this paper, we study the algebraic independence of psi(f1), ... , psi(fn) using a recent result of Medvedev and Scanlon. Related questions in transcendental number theory and canonical heights in arithmetic dynamics are also discussed.