Related papers: From Lyapunov modes to the exponents for hard disk…
Two approaches are presented for computing upper bounds on Lyapunov exponents and their sums, and on the Lyapunov dimension, among all trajectories of a dynamical system governed by ordinary differential equations. The first approach…
This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian L\'evy noise. In a suitable moving frame, the linearisation of such a system can be regarded as a small perturbation of a…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions.…
For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy…
We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to $L^{\mu s}$, where the…
We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…
In this article, we investigate the BV stability of $2\times 2$ hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing…
We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is…
The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed…
In this work we study the asymptotic behavior of a class of damped second-order gradient systems $$ \ddot{u}(t) + a\dot{u}(t) + \nabla W(u(t)) = 0, $$ under assumptions ensuring local convexity of the potential near equilibrium and…
Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to…
Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as~well as on a space of $p$-summable functions. The main result states that in…
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate…
This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency…
For a one-dimensional discrete Schr\"odinger operator with a weakly coupled potential given by a strongly mixing dynamical system with power law decay of correlations, we derive for all energies including the band edges and the band center…
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
The Lyapunov Characteristic Exponents are a useful indicator of chaos in astronomical dynamical systems. They are usually computed through a standard, very efficient and neat algorithm published in 1980. However, for Hamiltonian systems the…