## 126 Citations

### Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary

- MathematicsIndagationes Mathematicae
- 2018

### Sets of bounded discrepancy for multi-dimensional irrational rotation

- Mathematics
- 2014

We study bounded remainder sets with respect to an irrational rotation of the d-dimensional torus. The subject goes back to Hecke, Ostrowski and Kesten who characterized the intervals with bounded…

### Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

- Mathematics
- 2010

We study the basis property of systems of exponentials with frequencies belonging to ‘simple quasicrystals’. We show that a diophantine condition is necessary and sufficient for such a system to be a…

### The Surprising Accuracy of Benford’s Law in Mathematics

- MathematicsAm. Math. Mon.
- 2020

Benford’s law is proved to be an empirical “law” governing the frequency of leading digits in numerical data sets, and the observed behavior is related to classical results in Diophantine approximation as well as recent deep conjectures in this area.

### Weighted $$1\times 1$$1×1 Cut-and-Project Sets in Bounded Distance to a Lattice

- MathematicsDiscret. Comput. Geom.
- 2019

Recent results of Grepstad and Larcher are used to show that weighted cut-and-project sets are bounded distance equivalent to some lattice if the weight function h is continuous on the internal space, and if h is either piecewise linear, or twice differentiable with bounded curvature.

### Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems

- Mathematics
- 2013

A family of discontinuous symplectic maps arising naturally in the study of nonsmooth switched Hamiltonian systems is considered. This family depends on two parameters and is a canonical model for…

### On some oscillating sums

- Mathematics
- 2008

This paper deals with various properties (theoretical as well as computational) of the sums Sα(n) = ∑n j=1(−1) where α is any real number (mostly a positive real quadratic). Communicated by Michael…

### Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity

- Mathematics
- 2020

Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the…

### Diophantine properties of IETs and general systems: quantitative proximality and connectivity

- Mathematics
- 2013

AbstractThree properties of dynamical systems (recurrence, connectivity and proximality) are quantified by introducing and studying the gauges (measurable functions) corresponding to each of these…

### Discovering an infinite prime flow by finding a Proximal Orbit Dense flow

- Mathematics
- 2012

In this document, the proof of the existence of an infinite prime flow, by showing that a Proximal Orbit Dense flow is prime, is examined. This proof has been given by Furstenberg, Keynes and Shapiro…