The present paper deals with investigations on the distribution modulo 1 of sequences of powers of real (2 × 2)-matrices A in R4. It is proved that for almost all (in the sense of the Lebesgue measure in R4) such matrices possessing at least one (real or complex) eigenvalue with modulus larger than 1 the sequence (As(n))∞n=1 is uniformly distributed in R4 modulo 1, where (s(n))∞n=1 is an arbitrary fixed strictly increasing sequence of positive integers. Moreover, the inequality D(N) ≦ C(A, ε)N- 1 2(log N) 11 2 + ε (ε>0) is derived as an estimate for the discrepancy of the sequence (As(n)) for almost all real (2 × 2)-matrices A without real eigenvalues and with determinant larger than 1.
|Number of pages||12|
|Publication status||Published - 1 Dec 1981|
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