Topic
Minkowski's question mark function
About: Minkowski's question mark function is a research topic. Over the lifetime, 93 publications have been published within this topic receiving 1313 citations.
Papers published on a yearly basis
Papers
1 May 1960
64 citations
TL;DR: This paper surveys the main properties of functional operators, ---transfer operators--- due to Ruelle and Mayer that describe precisely the dynamics of the continued fraction transformation.
59 citations
TL;DR: In this article, various properties of continued fraction expansions of complex numbers in terms of Gaussian integers are described. But these properties can be arrived at through various algorithms, as also in a more general way than what we call “iteration sequences”.
Abstract: We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Such numerous distinct ex- pansions are possible for a complex number. They can be arrived at through various algorithms, as also in a more general way than what we call “iteration sequences”. We consider in this broader context the analogues of the Lagrange theorem characterizing quadratic surds, the growth properties of the denomi- nators of the convergents, and the overall relation between sequences satisfying certain conditions, in terms of non-occurrence of certain finite blocks, and the sequences involved in continued fraction expansions. The results are also ap- plied to describe a class of binary quadratic forms with complex coefficients whose values over the set of pairs of Gaussian integers form a dense set of complex numbers.
46 citations
TL;DR: In this article, it was shown that closed geodesies, when ordered by length, are equidistributed with respect to the Poincare measure, and the main application of this result is to distribution of quadratic irrationals in the unit interval with an appropriate ordering.
Abstract: In this note we show that closed geodesies, when ordered by length, are equidistributed with respect to the Poincare measure. Our main application of this result is to distribution of quadratic irrationals in the unit interval with respect to an appropriate ordering.
44 citations
TL;DR: In this article, a family of continuous, strictly increasing singular functions on the unit interval is introduced and the Hausdorff dimension of the set of points where the singular functions have nonvanishing derivatives is investigated.
36 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 3 |
| 2019 | 3 |
| 2018 | 3 |
| 2017 | 3 |
| 2016 | 3 |