Related papers: Thick attractors with intermingled basins
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
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…
We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical…
Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
Metriplectic dynamics couple a Poisson bracket of the Hamiltonian description with a kind of metric bracket, for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the \emph{basic reproduction number} $\mathcal{R}_0 < 1$ is not sufficient to guarantee the elimination of…
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak…
In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…
We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their…
A new intrinsic metric called $t$-metric is introduced. Several sharp inequalities between this metric and the most common hyperbolic type metrics are proven for various domains $G\subsetneq\mathbb{R}^n$. The behaviour of the new metric is…
We describe a class of fractal attractors induced by \beta-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log \beta and have an ergodic measure of full entropy. Moreover we determine the…
Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However,…
Hydrodynamic attractors have recently gained prominence in the context of early stages of ultra-relativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of…
We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from the loc.cit., in particular, the geometry…
We introduce the concepts of Baire Ergodicity and Ergodic Formalism, employing them to study topological and statistical attractors. Specifically, we establish the existence and finiteness of such attractors and provide applications for…