150 citations · 848 across the 43 of their papers we have counts for
6 papers · 1 filter
On the ergodic theory of Tanaka-Ito type alpha-continued fractions
Hitoshi Nakada, Wolfgang Steiner
We show the ergodicity of Tanaka-Ito type -continued fraction maps and construct their natural extensions. We also discuss the relation between entropy and the size of the natur…
Discrepancy Skew Products and Affine Random Walks
Jon. Aaronson, Michael Bromberg, Hitoshi Nakada
We prove bounded rational ergodicity for some discrepancy skew products whose rotation number has bad rational approximation. This is done by considering the asymptotics of associa…
On multiple recurrence and other properties of "nice" infinite measure preserving transformations
Jon Aaronson, Hitoshi Nakada
We discuss multiple versions of rational ergodicity and rational weak mixing for "nice" transformations, including Markov shifts, certain interval maps and hyperbolic geodesic flow…
Farey map, Diophantine approximation and Bruhat-Tits tree
Dong Han Kim, Seonhee Lim, Hitoshi Nakada +1
Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents, we continue the study of the Gauss map via Farey maps to contain all the in…
Generalized Brjuno functions associated to -continued fractions
Laura Luzzi, Stefano Marmi, Hitoshi Nakada +1
For αin the interval [0,1], we consider the one-parameter family of α-continued fraction maps, which include the Gauss map (α=1) and the nearest integer (α=1/2) and by-excess (α=0)…
On the mixing coefficients of piecewise monotonic maps
Jon Aaronson, Hitoshi Nakada
We investigate the mixing coefficients of interval maps satisfying Rychlik's conditions. A mixing Lasota-Yorke map is reverse -mixing. If its invariant density is uniformly boun…