Related papers: Multifractal invariant measures in expanding piece…
Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of…
We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the…
In this paper, we determine the almost sure multifractal spectrum of a class of random functions constructed as sums of pulses with random dilations and translations. In addition, the continuity modulii of these functions is investigated.
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the mixed multifractal spectra of Birkhoff averages of countably many…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…
Modern biological techniques such as Hi-C permit to measure probabilities that different chromosomal regions are close in space. These probabilities can be visualised as matrices called contact maps. In this paper, we introduce a…
We apply multifractal analysis to an experimentally obtained quasi-two-dimensional crystal with fourfold symmetry, in order to characterize the sidebranch structure of a dendritic pattern. In our analysis, the stem of the dendritic pattern…
This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…
We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
We propose nonparametric open-end sequential testing procedures that can detect all types of changes in the contemporary distribution function of possibly multivariate observations. Their asymptotic properties are theoretically investigated…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
We study self-similar measures in $\mathbb{R}$ satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a measure $\mu$, we show that there is a finite set of concave…
We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set.…
For a map $f:X \to M$ into a manifold $M$, we study the sets of deficient and multiple points of $f$. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in $X$, and we also provide…
Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity,…
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important…
We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that $X\subset Y$, although no such coupling can be invariant. Here,…