相关论文: Chaos for Cowen-Douglas operators

In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…

Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…

Chaos synchronization in one of charge-carrier dynamical systems in photoconductors is studied within both the replica and nonreplica approaches.It has been shown that using the boundedness of the solutions of the dynamical systems,…

We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…

This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic…

The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect…

Let T be a Cowen-Douglas tuple on a Banach space X. We use functional representations of T to associate with each T-invariant subspace Y of X an integer called the fiber dimension of Y. Among other results we prove a limit formula for the…

While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this convergence for a particular equation with quadratic…

We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given a smooth closed domain $D\in\mathbb{R}^2$, a central mass generates a Keplerian…

Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…

We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution…

We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator…

We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators.

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…

We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$ ($\kappa\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be…

Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both…

We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the…

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…

In this paper, we demonstrate conditions under which a Lindel\"{o}f dynamical system exhibits $\omega$-chaos. In particular, if a system exhibits a generalized version of the specification property and has at least three points with…

We consider the dynamical problem for a system of three particles in which the inter-particle forces are given as the gradient of a Lennard-Jones type potential. Furthermore we assume that the three particle array is subject to the…