70 citations · 247 across the 23 of their papers we have counts for
24 papers
Quantization dimensions of negative order
Marc Kesseböhmer, Aljoscha Niemann
We investigate the possibility of defining meaningful upper and lower quantization dimensions for a compactly supported Borel probability measure of order , including negative v…
Exact asymptotic order for generalised adaptive approximations
Marc Kesseböhmer, Aljoscha Niemann
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function defined on dyadic cubes.…
Approximation order of Kolmogorov diameters via -spectra and applications to polyharmonic operators
Marc Kesseböhmer, Aljoscha Niemann
We establish a connection between the -spectrum of a Borel measure on the -dimensional unit cube and the approximation order of Kolmogorov diameters of the unit spher…
Thermodynamic formalism for transient dynamics on the real line
Maik Gröger, Johannes Jaerisch, Marc Kesseböhmer
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic -extensions of expanding interval maps.…
Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails
Marc Kesseböhmer, Tanja Schindler
On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails and fulfilling a mild mixing condition. We…
Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata
Marc Kesseböhmer, Jens D. M. Rademacher, Dennis Ulbrich
In this paper we analyse the non-wandering set of 1D-Greenberg-Hastings cellular automata models for excitable media with excited and refractory state…
Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type
Marc Kesseböhmer, Tanja Schindler
We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only…
Diffraction of return time measures
Marc Kesseböhmer, Arne Mosbach, Tony Samuel +1
Letting denote an ergodic transformation of the unit interval and letting denote an observable, we construct the -weighted return time measure…
Strong laws of large number for intermediately trimmed Birkhoff sums of observables with infinite mean
Marc Kesseböhmer, Tanja Schindler
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we gener…
A multifractal analysis for cuspidal windings on hyperbolic surfaces
Johannes Jaerisch, Marc Kesseböhmer, Sara Munday
In this paper we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp winding number. We will comp…
Regularity of aperiodic minimal subshifts
Fabian Dreher, Marc Kesseböhmer, Arne Mosbach +2
At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearl…
Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean
Marc Kesseböhmer, Tanja Schindler
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the…
Escape rates for special flows and their higher order asymptotics
Fabian Dreher, Marc Kesseböhmer
In this paper escape rates and local escape rates for special flows are sudied. In a general context the first result is that the escape rate depends monotonically on the ceiling f…
A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory
Mark Kesseböhmer, Sabrina Kombrink
We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet se…
A classification of aperiodic order via spectral metrics and Jarník sets
Maik Gröger, Marc Kesseböhmer, Arne Mosbach +2
Given an and a with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope with respect to (i) an -Höder regula…
A note on measure-geometric Laplacians
Marc Kesseböhmer, Tony Samuel, Hendrik Weyer
We consider the measure-geometric Laplacians with respect to atomless compactly supported Borel probability measures as introduced by Freiberg and Zähle in 2002 and show…
On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps
Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel
We consider a family of Markov interval maps interpolating between the Tent map and the Farey map . Letti…
Induced topological pressure for countable state Markov shifts
Johannes Jaerisch, Marc Kesseböhmer, Sanaz Lamei
We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. F…
Wavelets for iterated function systems
Jana Bohnstengel, Marc Kesseböhmer
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume th…
Regularity of multifractal spectra of conformal iterated function systems
Johannes Jaerisch, Marc Kesseböhmer
We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously o…
The arithmetic-geometric scaling spectrum for continued fractions
Johannes Jaerisch, Marc Kesseböhmer
To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifr…
Sets of non-differentiability for conjugacies between expanding interval maps
Thomas Jordan, Marc Kesseböhmer, Mark Pollicott +1
We study differentiability of topological conjugacies between expanding piecewise interval maps. If these conjugacies are not , then they have zero derivative almost…
A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We…
A distributional limit law for the continued fraction digit sum
Marc Kesseböhmer, Mehdi Slassi
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit…