Related papers: Invariant scrambled sets, uniform rigidity and wea…
We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter \epsilon (0 < \epsilon < 1/4). The dynamical system considered is chaotic and unsynchronized for this…
The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…
We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set K is contained in a locally invariant center submanifold if and only if each strong stable…
In this paper we focus on Bratteli-Vershik models of general compact zero-dimensional systems with the action of a homeomorphism. An ordered Bratteli diagram is called decisive if the corresponding Vershik map prolongs in a unique way to a…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…
We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t),…
We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval $T_{\beta}(x)=\beta x$ (mod $1$), $x\in[0,1]$, $\beta>0$, which are the so-called…
We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the…
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
Mixtures of near-symmetric oppositely charged components with strong attractive short range interactions exhibit ordered lamellar phases at low temperatures. In the strong segregation limit the state of these systems can be described by the…
This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The It\^o or Stratonovich stochastic differential equations with the Wiener…
We consider the Cauchy problem for first order systems. Assuming that the set of the singular points of the characteristic variety is a smooth manifold and the characteristic values are real and semi-simple we introduce a new class which is…
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those…