11H71 26A46 2 93B1 1 93B17 1 \(\Delta^{\mu}\)-representation 1 continuous transformation of \((0,1]\) preserving ``tails'' of \(\Delta^{\mu}\)-representation of numbers 1 continuous transformation of interval 1 cylinder 1 function preserving ``tails'' of \(\Delta^{\mu}\)-representation of numbers 1 left and right shift operators 1 tail of representation of number 1 tail set 1 two-symbol system of encoding for real numbers with two bases having different signs (\(G_2\)-representation) 1