Related papers: Holder regularity and chaotic attractors
This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…
We consider a family of Leray-$\alpha$ models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter $\theta$, of the Navier-Stokes equations. In particular, they share…
We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be…
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of operators. We establish the Caccioppoli-type inequality with…
A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…
In this paper we study both experimentally and numerically the intermittent behavior taking place near the boundary of the synchronous time scales of chaotic oscillators being in the regime of time scale synchronization. We have shown that…
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The Parameter Switching (PS) algorithm is utilized, which switches the control parameter within a given set of…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out…
We characterize when a compact, invariant, asymptotically stable attractor on a locally compact Hausdorff space is a strong deformation retract of its domain of attraction.
We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with…
The asymptotic sectional hyperbolicity is a weak notion of hyperbolicity that extends properly the sectional-hyperbolicity and includes the Rovella attractor as a archetypal example. The main feature of this definition is the existence of…
We consider the Hall effect in a system of weakly coupled one-dimensional chains with Luttinger interaction within each chain. We construct a perturbation theory in the inter-chain hopping term and find that there is a power law dependence…
An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…
Transport through a Hubbard chain of size N (=1,2,3,...) connected to reservoirs is studied at T = 0 in an electron-hole symmetric case based on the second-order perturbation theory in U. The result shows a typical even-odd property…
We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of $C^{1,\alpha}$ submanifolds, possibly with multiplicity, meeting tangentially, given that the…
We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their…
We examine a class of one-dimensional lattice-gases characterised by a gradient condition which guarantees the existence of Gibbs-type homogeneous stationary states. We show how, defining appropriate boundary conditions, this leads to a…
We propose that the inhomogeneous patterns seen by STM in some underdoped superconducting cuprates could be related to a bond-order-wave instability of the staggered flux state, one of the most studied "normal" state proposed to compete…
This paper demonstrates the stability of the global regularity for a class of pseudo-differential operators under lower-order perturbations. We establish that if an operator has a globally hypoelliptic symbol, its global regularity (in the…