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FINITENESS AND PERIODICITY OF BETA EXPANSIONS -NUMBER THEORETICAL AND DYNAMICAL OPEN
 

Summary: 1
FINITENESS AND PERIODICITY OF BETA EXPANSIONS -
NUMBER THEORETICAL AND DYNAMICAL OPEN
PROBLEMS
SHIGEKI AKIYAMA (NIIGATA UNIVERSITY, JAPAN)
Let y = f(x) be a positive real function. Consider a digital expansion of a real
number x in a form:
x = 0 + f(1 + f(2 + f(3 + . . . .
given by an algorithm with 0 = x , r0 = x - x and
n+1 = f-1
(rn) , rn+1 = f-1
(rn) - f-1
(rn) .
This is R´enyi's f-expansion ([24]). It is the usual b-adic expansion when f(x) =
x/b and the regular continued fraction when f(x) = 1/x. For f(x) = x/ with a
non-integer > 1, it is called the -expansion.
0.2 0.4 0.6 0.8 1
0.2
0.4
0.6

  

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

 

Collections: Mathematics