Related papers: Non-hyperbolic Iterated Function Systems: attracto…
In this paper, we analyze the smoothness and stability of hidden variable recurrent fractal interpolation functions (HVRFIF) with function contractivity factors introduced in Ref. 1. The HVRFIF is a hidden variable fractal interpolation…
We study Non-autonomous Iterated Function Systems (NIFSs) with overlaps. A NIFS on a compact subset $X\subset\mathbb{R}^m$ is a sequence $\Phi=(\{\phi^{(j)}_{i}\}_{i\in I^{(j)}})_{j=1}^{\infty}$ of collections of uniformly contracting maps…
We prove that impulsive systems, which possess an ISS Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
Let $0< \lambda < \mu<1$ and $\lambda+\mu>1$. In this note we prove that for the vast majority of such parameters the top of the attractor $A_{\lambda,\mu}$ of the IFS $\{(\lambda x,\mu y), (\mu x+1-\mu, \lambda y+1-\lambda)\}$ is the graph…
In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated…
In this paper, we study the limit measures of the empirical measures of Lebesgue almost every point in the basin of a partially hyperbolic attractor. They are strongly related to a notion named Gibbs u-state, which can be defined in a large…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…
In this paper, we focus on the packing measure of self-similar sets. Let $K$ be a self-similar set whose Hausdorff dimension and packing dimension equal $s$, we state that if $K$ satisfies the strong open set condition with an open set…
We establish the effective {\em finite dimensionality} of the dynamics corresponding to a flow-plate interaction PDE model arising in aeroelasticity: a nonlinear panel, in the absence of rotational inertia, immersed in an inviscid potential…
This is the second part of our study of the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on ${\Bbb R}^d$. In the first part we proved that the upper box-counting dimension of the attractor of any $C^1$ IFS on…
In this paper, we introduce and investigate the notions of Mean Dimension and Metric Mean Dimension for generalized iterated function systems (IFS). We establish basic properties of these invariants and prove that Mean Dimension is always…
Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…
Cabrelli, Forte, Molter and Vrscay in 1992 considered a {fuzzy} version of the theory of iterated function systems (IFSs in short) and their fractals%The idea was to extend the classical Hutchinson-Barnsley operator to selfmaps of a metric…
The present work provides two alternatives to formulate time-discounted incremental input/output-to-state stability (i-IOSS) as a suitable detectability notion for general nonlinear systems with non-additive disturbances. Both formulations…
IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
This study presents an innovative approach to chaotic attractor stabilization introducing a memristor in discrete dynamical systems. Using the H\'enon map as a test case, we replace a system parameter with a memristive function governed by…
Some invariant sets may attract a nearby set of initial conditions but nonetheless repel a complementary nearby set of initial conditions. For a given invariant set $X\subset\R^n$ with a basin of attraction $N$, we define a stability index…