Related papers: Refined measurable rigidity and flexibility for co…
For a fixed topological Markov shift, we consider measure-preserving dynamical systems of Gibbs measures for 2-locally constant functions on the shift. We also consider isomorphisms between two such systems. We study the set of all…
In this note we give a simple sufficient condition for an affine iterated function system to admit an invariant affine subspace persistently with respect to changes in the translation parameters. This yields further examples of tuples of…
In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition, the dimension equals to the…
For various engineering and industrial applications it is desirable to realize mechanical systems with broadly adjustable elasticity to respond flexibly to the external environment. Here we discover a topology-correlated transition between…
In their comment, Murphy et al. (arxiv:0708.3677) criticize the fitting procedure we used in two previous papers [Srianand et al. 2004(Paper I) and Chand et al. 2004 (Paper II)] and conclude that the above papers offers no stringent test to…
In this paper, we consider entropy spectra on topological Markov shifts. We prove that if two measure-preserving dynamical systems of Gibbs measures with H\"older continuous potentials are isomorphic, then their entropy spectra are the…
We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
In this work, the issue of estimation of reachable sets in continuous bimodal piecewise affine systems is studied. A new method is proposed, in the framework of ellipsoidal bounding, using piecewise quadratic Lyapunov functions. Although…
The aim of the present paper is twofold. We study directed porosity in connection with conformal iterated function systems (CIFS) and with singular integrals. We prove that limit sets of finite CIFS are porous in a stronger sense than…
We study locally constant skew-product maps over full shifts of finite symbols with arbitrary compact metric spaces as fiber spaces. We introduce a new criterion to determine the density of leaves of the strong unstable (and strong stable)…
We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension…
A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb{R}^d$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension equal to the…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…