Exponential Diophantine approximation and symbolic dynamics

Abstract

We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of polynomials possibly having multiple roots. We derive several consequences of this formula, which are expected on the Markoff-Lagrange spectrum.

Minor changes and corrections after the referee report