| This thesis studies the rate of convergence of purely periodic continued fractions, and gives an explicit formula for calculating it. It also generalizes the concept to calculate the rate of convergence of any continued fraction. It relates the rate of convergence of any continued fraction gamma = [0; a1,a2,...] to its Lyapunov exponent lambdagamma, and to its Bn(gamma), where B0 = 1, B1 = a1, and Bn = a nBn-1 + Bn -2.; It is proved in this thesis that the rate of convergence of any infinite continued fraction is always less than or equal to 5-12 2 ≈ 0.38196601. Also this thesis provides a procedure to approximate a dense set of rates of convergence by rates of convergence of purely periodic continued fractions.; It is known that almost all continued fractions are distributed according to the Gauss measure. This thesis studies the probability of occurrence of any block of any length in their representation, and the chaotic behavior of their orbits.; Finally, this thesis uses dynamical systems techniques to prove already known results in continued fractions. |
