On Khintchine exponents and Lyapunov exponents of continued fractions

Abstract Assume that x ∈[0,1) admits its continued fraction expansion x =[ a 1 ( x ), a 2 ( x ),…]. The Khintchine exponent γ ( x ) of x is defined by $\gamma (x):=\lim _{n\to \infty }({1}/{n}) \sum _{j=1}^n \log a_j(x)$ when the limit exists. The Khintchine spectrum dim E ξ is studied in detail, wh... View More