19 citations · 75 across the 15 of their papers we have counts for
10 papers · 1 filter
Statistics and modelling of order patterns in univariate time series
Christoph Bandt
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of fo…
New relatives of the Sierpinski gasket
Christoph Bandt, Dmitry Mekhontsev
By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nat…
A single fractal pinwheel tile
Christoph Bandt, Dmitry Mekhontsev, Andrei Tetenov
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based o…
The two-dimensional density of Bernoulli Convolutions
Christoph Bandt
Bernoulli convolutions form a one-parameter family of self-similar measures on the unit interval. We suggest to study their two-dimensional density which has an intricate combinato…
Polynomial approximation of self-similar measures and the spectrum of the transfer operator
Christoph Bandt, Helena Peña
We consider self-similar measures on The Hutchinson operator acts on measures and is the dual of the transfer operator which acts on continuous functions. We d…
Finite orbits in multivalued maps and Bernoulli convolutions
Christoph Bandt
Bernoulli convolutions are certain measures on the unit interval depending on a parameter between 1 and 2. In spite of their simple definition, they are not yet well understood…
Conjugacies provided by fractal transformations I : Conjugate measures, Hilbert spaces, orthogonal expansions, and flows, on self-referential spaces
Christoph Bandt, Michael Barnsley, Markus Hegland +1
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measure…
Local structure of self-affine sets
Christoph Bandt, Antti Käenmäki
The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self…
Differentiability of fractal curves
Christoph Bandt, Alexey Kravchenko
While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. Ther…
Combinatorial topology of three-dimensional self-affine tiles
Christoph Bandt
We develop tools to study the topology and geometry of self-affine fractals in dimension three and higher. We use the self-affine structure and obtain rather detailed information a…