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Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is…
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…
In this work we propose a definition of an Euroattractor: an attracting invariant measure of a certain iterated functions system (IFS). An IFS is defined by specifying a set of functions, defined in subsets of R^N or in a classical phase…
The aim of this paper is to study the robustness of the family of pullback attractors associated to a non-autonomous coupled system of strongly damped wave equations, given by the following evolution system $$\left\{ \begin{array}{lr}…
This survey is a presentation of the arguments in the proof that Henon-like maps f_a(x,y)=(1-a x^2,0) + R(a,x,y) with |R(a,x,y)|< b have a "strange attractor", with positive Lebesgue probability in the parameter "a", if the perturbation…
We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of…
The aim of this work is to examine the upper-semicontinuity properties of the family of global attractors admitted by a non-isothermal viscous relaxation of some nonlocal Cahn-Hilliard equations. We prove that the family of global…
In this paper a periodic parameter switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor…
Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. While network architectures supporting sequence generation vary…
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…
In this paper we study arithmetic properties of a one-parameter family ${\mathbf H}$ of H\'enon maps over the affine line. Given a family of initial points ${\mathbf P}$ satisfying a natural condition, we show the height function…
We construct an iterated function system consisting of strictly increasing contractions $f,g\colon [0,1]\to [0,1]$ with $f([0,1])\cap g([0,1])=\emptyset$ and such that its attractor has positive Lebesgue measure.
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
The structure of the physical and strange attractors is inherently associated with the boundedness of fluctuations. The idea behind the boundedness is that a stable long-term evolution of any natural and engineered system is possible if and…
In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase.…
The velocity dependence of energy and momentum is studied. It is shown that in the case of STR in the space-time of only one spatial dimension the standard energy and momentum definition can be naturally modified without lost of local…
The behaviour of the 2D model system - the Ikeda map - is investigated in the weakly dissipative regime under external forcing on the incommensurate frequency. Coexistence of a large number of stable invariant curves is shown. Dependence of…