TY - JOUR

T1 - A realization of the Pascal automorphism in the concatenation graph and the sum-of-digits function s_2(n)

AU - Lodkin, A.A.

AU - Manaev, I.E.

AU - Minabutdinov, A.R.

PY - 2013

Y1 - 2013

N2 - A class of concatenation dynamical systems is introduced. Various automorphisms, including the Morse and the Pascal automorphisms, can be regarded as automorphisms of this class. In this realization, a natural number-theoretic interpretation of the problem whether the spectrum of an automorphism is discrete arises. In particular, the known character of the asymptotic behavior of the function $s_2(n)$ allows one to immediately see the non-discreteness of the spectrum of the Morse automorphism and to give a new formulation of the discreteness problem in the case of the Pascal automorphism.

AB - A class of concatenation dynamical systems is introduced. Various automorphisms, including the Morse and the Pascal automorphisms, can be regarded as automorphisms of this class. In this realization, a natural number-theoretic interpretation of the problem whether the spectrum of an automorphism is discrete arises. In particular, the known character of the asymptotic behavior of the function $s_2(n)$ allows one to immediately see the non-discreteness of the spectrum of the Morse automorphism and to give a new formulation of the discreteness problem in the case of the Pascal automorphism.

KW - Pascal automorphism

KW - concatenation dynamical system

KW - spectrum of an automorphism

KW - $s_2(n)$ function

KW - sum-of-digits function

U2 - 10.1007/s10958-013-1261-5

DO - 10.1007/s10958-013-1261-5

M3 - Article

VL - 190

SP - 459

EP - 463

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 3

ER -