Dynamics of complex continued fraction
speaker: Seonhee Lim (Seoul National University)abstract: The distributional analysis of Euclidean algorithms was carried out by Baladi and Vallée. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the set of rational numbers with bounded denominator based on the transfer operator methods. We extend their result to the Euclidean algorithm over appropriate imaginary quadratic fields by studying dynamics of the nearest integer complex continued fraction map, which is piecewise analytic and expanding but not a full branch map. By observing a finite Markov partition with a regular CW-structure, which enables us to associate the transfer operator acting on a direct sum of spaces of C1-functions, we obtain the limit Gaussian distribution as well as residual equidistribution. (This is joint work with Doheyong Kim and Jungwon Lee.)
timetable:
Thu 23 May, 9:00 - 10:00, Aula Dini
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