## Abstract

The present paper deals with investigations on the distribution modulo 1 of sequences of powers of real (2 × 2)-matrices A in R^{4}. It is proved that for almost all (in the sense of the Lebesgue measure in R^{4}) such matrices possessing at least one (real or complex) eigenvalue with modulus larger than 1 the sequence (A^{s(n)})^{∞}_{n=1} is uniformly distributed in R^{4} 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 (A^{s(n)}) for almost all real (2 × 2)-matrices A without real eigenvalues and with determinant larger than 1.

Original language | German |
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Pages (from-to) | 219-230 |

Number of pages | 12 |

Journal | Indagationes Mathematicae |

Volume | 43 |

Issue number | 2 |

Publication status | Published - 1 Dec 1981 |

## ASJC Scopus subject areas

- Mathematics(all)