MATHEMATICS
RESEARCH
INTERESTS AND EXPERTISE
Geometric
measures,
dimension theory and fractals (28A75,
28A78, 28A80)
Metric theory of numbers
(11K50, 11K55)
Dynamical systems and
ergodic theory (37A30,37A35,37C40,
37C45, 37C70)
Random walks (60G50)
General mathematics (00A05,
00A06, 00A20, 00A22)
Calculation
and approximation of invariant densities (37C40)
Infinite self-similar and
self-affine carpets (28A80)
Representations of real numbers /
generalized continued fractions (11K55)
Random walks with periodic
steps (60G50)
Generalized Somos' constants (11K55)
Monotony of the Garsia
entropy (37A35)
REFEREED
ARTICLES
26.
Representations of real
numbers induced by probability distributions on $\mathbb{N}$ (pdf)
Tatra Mt. Math. Publ. 81, 1–8, 2022.
25. On the universality of Somos' consstant (pdf)
Elemente der Mathematik, 77, 138-141, 2022.
24. Non-uniform expansions of
real numbers (pdf)
Mediterranean Journal of Mathematics, 18 (2), 1-8, 2021.
23.
Random walks on Z with exponentially increasing step length and
Bernoulli convolutions (pdf)
Rocky Mountain Journal
of Mathematics, vol 49, no. 6, 1993-2003,
2019.
22. Fractal
attractors induced by $\beta$-shifts (pdf)
Chaos,
Solitons & Fractals, vol 123, 87-90, 2019.
21. Dimensional theoretical results
for a family generalized continued fractions (pdf)
Bulletin Polish Acad. Sci. Math, vol 66, no. 2,
115-122, 2018.
20. Continued logarithm
representation of real numbers (pdf)
Real Analysis Exchange, vol 42, no.1,
57-66,
2018.
19. Return
of Fibonacci walks (pdf)
Statistics and Probability Letters, vol. 121, 51-53, 2017.
18. Nonuniform Markov geometric
measures (pdf)
Communication in Mathematical Analysis, vol. 18, no. 1,
36–47, 2015.
17.
Multifractality of
overlapping non-uniform self-similar measures (pdf)
Monatshefte für Mathematik, vol. 177, issue 3, 461-468, 2015.
16. Geometric series with
randomly
increasing exponents (pdf)
Archiv der Mathematik, vol. 102, no. 3, 283-291, 2014.
15. Absolutely continuous
random
power series in reciprocals of Pisot numbers (pdf)
Statistics and Probability Letters, vol. 83,
issue 2, 431–435, 2013.
14. Dimension estimates for certain
sets of infinite complex continued fractions (pdf)
Journal of Mathematics, vol. 2013, 1-5, 2013.
13. On the Hausdorff dimension of fractals given by certain expansions
of real numbers (pdf)
Archiv der Mathematik, vol. 97, no. 5, 459-466,
2011.
12.
A family of exceptional
parameters for non-uniform self-similar measures (pdf)
Electronic Communications in Probability, vol.
16, 192-199,
2011.
11. On
inhomogeneous Bernoulli convolution and random power series (pdf)
Real Analysis Exchange, vol 36, no.1, 213-222,
2011. (with A.
Bisbas).
10. Li-Yorke pairs of full Hausdorff dimension for some chaotic
dynamical systems (pdf)
Mathematica Bohemica,
135,
no. 3
,
279–289, 2010.
9. The weighted
Moran formula for the dimension of generic McMullen-Bedford carpets (pdf)
Chaos,
Solitons & Fractals, vol. 42, issue 2,
890-895, 2009.
8. A general result on
absolute continuity of non-uniform self-similar measures on the real
line (pdf)
Fractals, vol. 16, no. 4,
299-304, 2008 .
7.
Random walks on infinite self-similar graphs (pdf)
Electronic Journal of Probability, vol.12, no. 46, 1258-1275,
2007.
6.
Dimension theory for linear solenoids (pdf)
Fractals, vol. 15, no. 1, 63-72, 2007.
5. A
construction of singular overlapping
self-similar measures (pdf)
Acta Mathematica Hungarica, vol. 113
(4-4),333-343, 2006.
4.
Dimension
theoretical properties of
generalized Baker's transformations (pdf)
Nonlinearity 15,
1299-1307, 2002.
3.
Number theoretical peculiarities in the dimension
theory of dynamical systems (pdf)
Israel
Journal of Mathematics 128, 267-283, 2002.
2. An
isomorphism between polynomial eigenfunctions
of the transfer operator and the Eichler cohomology for modular groups (pdf)
Mathematical Physics Electronic Journal, vol. 7, 1-18, 2001. (with D.
Mayer)
1.
Properties of some overlapping self-similar and
some self-affine measures (pdf)
Acta Mathematica Hungarica, vol.
92 (1-2), 143-161, 2001.
PREPRINTS
On the dimension of certain sets
araising in the base two expansion (pdf)
submitted, 2022.
Expansions of real numbers with respect to two integer bases (pdf)
submitted after revison, 2021.
Singular Bernoulli
convolutions for non-Pisot numbers (pdf)
permanent preprint
REPORTS
Dimensional theoretical properties of affine
dynamical systems (pdf)
DFG-Schwerpunktprogramm "`Dynamik:
Analysis, effiziente Simulation und Ergodentheorie", vol. 5, 1-10, 2000.
A new class of counterexamples to
the variational
principle for Hausdorff dimension
DFG-Schwerpunktprogramm
"Dynamik: Analysis, effiziente Simulation und Ergodentheorie", vol. 25,
1-15 1998.
THESIS
Dimensional
theoretical
properties of some affine
dynamical systems (pdf)
PhD Thesis, Free University
Berlin, 1999.
Die Fat Baker's
Transformation - Ein Gegenbeispiel
zum Variationsprinzip der Hausdorff Dimension (pdf)
Diploma Thesis, Free University of Berlin, 1996.
TALKS
Dimension theory of
representations of real numbers
University Braunschweig, 2019. (pdf)
Ernst-Abbe-Hochschule Jena, 2018. (pdf)
Queen Mary University of London, 2015. (pdf)
Leuphana University Lüneburg, 2014.
(pdf)
Multifractal analysis of
self
similar measures (pdf)
Die Methode der
kleinsten Quadrate (pdf)
Ernst-Abbe-Hochschule Jena, 2018.
About Li-Yorke chaos from
a dimensional theoretical perspective (pdf)
Symposium on Ergodic Theory and Dynamical Systems, England, 2012.
Visegrad Conference, Slovakia, 2011.
Elementare
Zeitreihenanalyse (pdf)
HTW Berlin, 2011.
From number theory to
dynamical systems via geometric measure theory (pdf)
Queen Mary University of London, 2010.
Zufallswege auf unendlichen gewurzelten selbst-ähnlichen
Graphen (pdf)
University Erlangen-Nürnberg, 2010.
Results on
self-similar measures on the real line (pdf)
Conference "CODY Mid-term", England, 2009.
Conference "Fractal Geometry and Stochastics", Germany, 2008.
Der T-Test (pdf)
University Mainz, 2008.
Random walks on infinite
self-similar graphs (pdf)
University Greifswald, 2008
Conference "Ergodic theory and dynamical systhems", Poland 2006,
Conference "Dynamical Systems", Czech
Republic, 2006.
Einführung in
die Dimensionstheorie
Dynamischer Systeme (pdf)
University Konstanz, 2003.
Results on
self-similar measure and applications (pdf)
University Greifswald, 2003,.
University Koblenz, 2003.
Dimensions
theory for Attractors of Solenoid-Typ (pdf)
DMV Conference, Germany, 2002.
University Hamburg, 2002.
An result on overlapping
self-similar measures and
its applications
University Lisbon, 2002.
Classical and
Semiclassical trace formulae
University Clausthal, 2001.
A Douady-Oesterle type
estimate for the Hausdorff
dimension of invariant sets of piecewise smooth maps
Conference "Differential Equations and Application", Russia,
2000.
University Dresden, 2000.
Erdös
measures
University Clausthal, 2000.
Dimension
theory of affine Systems,
University Clausthal, 2000.
Workshop "Dimension of attractors", University St. Petersburg, 1999.
University Dresden, 1999.
On the
variational principle for Hausdorff
dimension
University Dresden, 1999,
University Lisbon 1999.
Symbolic dynamics and its
applications
Free University Berlin, 1999.
Properties of some
self-similar and self-affine
measures
Workshop "Around one dimensional dynamics", Banach
Center Warszawa, 1997.
Algorithms
Lecture, HAWK Göttingen, 2023.
Probability
theory and numerics
Lecture, HAWK Göttingen, 2022/23.
Advanced calculus
Lecture, HAWK Göttingen, 2022/23.
Introduction to the philsophy of mathematics
Lecture, Technical University Braunschweig, 2022.
Beautiful mathematical theorems - an
overview -
Lecture, Technical University Braunschweig, 2021/22.
Introduction to the philsophy of
mathematics
Lecture, Technical University Braunschweig, 2021.
Beautiful mathematical theorems - an
overview -
Lecture, Technical University Braunschweig, 2020/21.
Probability theory and statistic
Lecture, Leibniz University Hannover, 2017/18.
Lecture,
Leibniz University Hannover, 2017.
Lecture, Leibniz University Hannover, 2016/17.
Lecture,
Leibniz
University Hannover, 2016.
Analysis I
Lecture, Leuphana University Lüneburg, 2015.
Fractal geometry
Lecture, Leuphana University Lüneburg, 2015.
History and philosphy of Mathematics
Lecture, Leuphana University Lüneburg, 2015
Beautiful mathematical
theorems – an overview -
Lecture, Leuphana University Lüneburg, 2015
Cryptography
Lecture, Leuphana University Lüneburg, 2014/15
Linear Algebra
Lecture, Leuphana University Lüneburg, 2014/15
Topology
Lecture, Leuphana University Lüneburg, 2014/15
Analysis III
Lecture, Leuphana University Lüneburg, 2014/15
Fractal geometry
Lecture, Leuphana University Lüneburg, 2014.
Algebraic curves
Lecture, Leuphana University Lüneburg, 2014.
Dynamical systems
Lecture, Leuphana University Lüneburg, 2014.
Topology and Functionalanalysis
Lecture, Leuphana University Lüneburg, 2014.
Probability
theory and cryptography
Lecture, University of Apllied Science Berlin, 2011/2012.
Lecture, University of Apllied Science Berlin, 2010/2011.
Lecture, University of Apllied Science Berlin, 2009/2010.
Lecture, University of Apllied Science Berlin, 2008/2009.
Lecture, University of Apllied Science Berlin,
2006/2007.
Linear Algebra
Lecture, University of Apllied Science Berlin, 2011.
Mathematics for economist and chemist II
Lecture, University Clausthal, 2010.
Mathematics for economist
and chemist I
Lecture, University Clausthal, 2009/2010.
Analysis
Lecture, University of Apllied Science Berlin, 2008/2009.
Mathematics for
technicians
Lecture, University of Apllied Science Berlin, 2008.
Mathematics for engineers
Lecture, University of Apllied Science Berlin, 2007/2008.
Mathematics for compuer
scientists
Lecture, University of Apllied Science Berlin, 2007.
Lecture, University of Apllied Science Berlin, 2006.
Discrete mathematics
Lecture, University of Apllied Science Berlin, 2005/2006.
Mathematics and Physics
Courses, High School Hamburg,
2004 /2005 .
Introduction to dynamical
systems
Lecture, University Clausthal,
2002.
Dimsion theory
Lecture, University Clausthal, 2001/2002.
Ergodic theory
Lecture, University Dreden, 2000.
Statistic
Courses, Free University Berlin, 1995.
Linear Algebra I/II
Courses, Free Uinversity Berlin, 1993/94.
Analysis I-III
Courses, Free University Berlin, 1992/93