linear part

[y.kohmoto]

   [rough sketch of how it generates a linear sequence]

    LLI is defined as follows.
    a(n)=cof_2 ([(2+e)*a(n-1)+B]) ,
                        cof_2 (n) = n/2^r , 2^r is the highest power of 2
dividing n.

                        0<e<0.01 , B is a real number

    d(a(n))=a(n)-a(n-1)
           =cof_2 ([2*a(n-1)+e*a(n-1)+B])-a(n-1)

         If  fac_2 ([2*a(n-1)+e*a(n-1)+B]) = 2  then
           =[a(n-1)+e/2*a(n-1)+B/2]-a(n-1)
           =[e/2*a(n-1)+B/2]
                        fac_2 (n) = 2^r , 2^r is the highest power of 2
dividing n.

         If e/2 is small enough then [e/2*a(n-1)] becomes almost constant.
So,
           =C

    It means LLI has linear subsequences.

    LLI is an abbreviation of "a lot of linear parts which are isolated each
other".
    K is for "kimyo" which means strange in Japanese

    Yastoshi

     http://boat.zero.ad.jp/~zbi74583/another02.htm