Related papers: Stability of iterated function systems on the circ…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
We construct an integer-valued Lyapunov function $\sigma(\cdot)$ for generalized negative cyclic feedback system; and prove that $\sigma(\cdot)$ on any $\omega$-limit set which generated by Poincar\'{e} mapping of bounded solution of such…
It is well-known that the exponential stability of Integral Difference Equations and Delay Difference Equations, in the usual state space of continuous functions, is equivalent to the location of the roots of its associated characteristic…
A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$, reduce its coefficients mod $p$ and consider its action on the field $\mathbb{F}_p$. The questions of whether and…
Guided by classical concepts, we define the notion of \emph{ends} of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points…
Given a discrete-time random dynamical system represented by a cocycle of non-singular measurable maps, we may obtain information on dynamical quantities by studying the cocycle of Perron-Frobenius operators associated to the maps. Of…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable, then it is also asymptotically stable. The main assumptions are transversal nondegeneracy of the manifold of the ground states,…
In this paper, we study "demi-caract\'eristique" and (Poisson) stability in the sense of Poincar\'e. Using the definitions \'a la Poincar\'e for $\R$-actions $v$ on compact connected surfaces, we show that "$R$-closed" $\Rightarrow$…
We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In…
We formulate and prove a new criterion for stability of e-processes. It says that any e-process which is averagely bounded and concentrating is asymptotically stable. In the second part, we show how this general result applies to some shell…
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
We prove a parametric generalization of the classical Poincare-Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these…
This paper examines the stability of the \`a trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…