Name	Koshiro Ishimura
	Department	Department of Mathematics, School of Fundamental Science and Technology
	Research Fields	Ergodic theory

I study about mulitidimensional continued fraction algorithms and its ergodic properites. Recently I consider the 2 dimensional continued algorithm which is called the negative slope algorithm and it is induced from 3-interval exchange transformations. Generally quadratic irrational numbers have the periodic expansion with respect to the continued fraction algorithm. This also occur in the case of the multidimensional continued fraction algorithm. We construct the natural extension of the continued fraction algorithm, then we obtain the purely periodicity.

The arithmetic algorithm such a continued fraction algorithm gives the tiling in the Euclid space. I am interested in the tiling arising from the negative slope algorithm. It may be give something about 3-interval exchange transformations.