Related papers: The Lyapunov spectrum as the Newton-Raphson method…
We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…
A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon…
We prove that closed negatively curved locally symmetric spaces are characterized up to isometry among all homotopy equivalent negatively curved manifolds by the Lyapunov spectra of the periodic orbits of their geodesic flows. This is done…
Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the nonlocal velocity towards a given equilibrium velocity. Therefore, we present a Lyapunov function measuring the $L^2$ distance between these…
By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE)…
We show a linear response statement for fixed points of a family of Markov operators which are perturbations of mixing and regularizing operators. We apply the statement to random dynamical systems on the interval given by a deterministic…
We analyze the two-point motions of iterated function systems on the unit interval generated by expanding and contracting affine maps, where the expansion and contraction rates are determined by a pair $(M,N)$ of integers. This dynamics…
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 present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent…
This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus…
The problems on the location of the matrix spectrum inside or outside domains bounded by ellipses or parabolas are studied. Special Lyapunov-type equations are connected with these problems. Theorems about the unique solvability of such…
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…
Let $T$ be an expanding Markov map with a countable number of inverse branches and a repeller $\Lambda$ contained within the unit interval. Given $\alpha \in \R_+$ we consider the set of points $x \in \Lambda$ for which $T^n(x)$ hits a…
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
The Lagrange and Markov spectra have been studied since late 19th century, concerning badly approximable real numbers. The Mordell-Gruber spectrum has been studied since 1936, concerning the supremum of the area of a rectangle centered at…
This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an…
Previously Casetti, Clementi and Pettini [\textbf{Phys.Rev.E \textbf{54},6,(1996)}] have investigated the Lyapunov spectrum of Hamiltonian flows for several Hamiltonian systems by making use of the Riemannian geometry. Basically the…
Working with a general class of linear Hamiltonian systems specified on $\mathbb{R}$, we develop a framework for relating the Maslov index to the number of eigenvalues the systems have on intervals of the form $[\lambda_1, \lambda_2)$ and…