Related papers: Locating Ruelle-Pollicott resonances
Dynamics of a randomly-perturbed quantum system with 3/2-degrees of freedom is considered. We introduce a transfer operator being the quantum analogue of the specific Poincar\'e map. This map was proposed in (Makarov, Uleysky, J. Phys. A:…
We provide a phenomenological formula which describes the low-frequency optical absorption of charge carriers in disordered systems with localization. This allows to extract, from experimental data on the optical conductivity, the relevant…
This paper investigates multi-agent frequencybased patrolling of intersecting, circle graphs under conditions where graph nodes have non-uniform visitation requirements and agents have limited ability to communicate. The task is modeled as…
We study the exploitation of polarimetric diversity in passive multistatic radar for detecting moving targets. We first derive a data model that takes into account polarization and anisotropy of targets inherent in multistatic…
Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
In this article we analyze the state-of-the-art in multilateration - the family of localization methods enabled by the range difference observations. These methods are computationally efficient, signal-independent, and flexible with regards…
A graph-theoretic analysis is undertaken for a compendium of input-output (transfer) metrics of a standard discrete-time linear synchronization model, including lp gains, frequency responses, frequency-band energy, and Markov parameters. We…
Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect…
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
We develop spectral theorems for nonautonomous linear difference systems, considering different types of $\mu$-dichotomies, both uniform and nonuniform. In the nonuniform case, intriguing scenarios emerge -- that have been employed but…
We study the dynamics of the synchronization transition (ST) of one-dimensional coupled map lattices. For the Bernoulli map it was recently found by Ahlers and Pikovsky (Phys. Rev. Lett. {\bf 88}, 254101 (2002)) that the ST belongs to the…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neutral direction (this is a semiclassical limit), the spectrum…
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain…
The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…