Hausdorff dimension of certain sets arising in Engel continued fractions

Abstract

In the present paper, we are concerned with the Hausdorff dimension of certain sets arising in Engel continued fractions. In particular, the Hausdorff dimension of setsare completely determined, where i.m. means infinitely many, {bn(x)} n≥1 is the sequence of partial quotients of the Engel continued fraction expansion of x and φ is a positive function defined on natural numbers.2010 Mathematics Subject Classification. Primary: 11K50, 37E05; Secondary: 28A80.