On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.
The metrical theory of complex continued fractions
On metrical theory of diophantine approximation over imaginary quadratic field
On the Lenstra constant associated to the Rosen continued fractions
On metric Diophantine approximation in positive characteristic
Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations
Metric inhomogeneous Diophantine approximation on the field of formal Laurent series
Metric and arithmetic properties of mediant-Rosen maps
Semisimple extensions of irrational rotations
We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.
Mod 2 normal numbers and skew products
Let E be an interval in the unit interval [0,1). For each x ∈ [0,1) define dₙ(x) ∈ 0,1 by , where t is the fractional part of t. Then x is called a normal number mod 2 with respect to E if converges to 1/2. It is shown that for any interval E ≠(1/6, 5/6) a.e. x is a normal number mod 2 with respect to E. For E = (1/6, 5/6) it is proved that converges a.e. and the limit equals 1/3 or 2/3 depending on x.
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