相关论文: Stable laws for heavy-tailed observables on polyno…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…
We consider diffeomorphisms of compact Riemmanian manifolds which have a Gibbs-Markov-Young structures, consisting of a reference set $\Lambda$ with a hyperbolic product structure and a countable Markov partition. We assume polynomial…
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…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
Quadratic-bilinear (QB) systems arise in many areas of science and engineering. In this paper, we present a scalable approach for designing locally stabilizing state-feedback control laws and certifying the local stability of QB systems.…
Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick…
A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is quite large and…
We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law $v =…
This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system.…
This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS.We show that…
The problem of the existence of an analytic normal form near an equilibrium point of an area-preserving map and analyticity of the associated coordinate change is a classical problem in dynamical systems going back to Poincar\'e and Siegel.…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
The equilibrium behavior of binary mixtures can be understood through the competition of energy scales, which classifies their corresponding phase diagrams into distinct topological regimes (Types I-IV). However, in many soft-matter…
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
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…
We investigate a two-component mixture of resonantly interacting Fermi gases as a function of the ratio \kappa of the heavy to the light mass of the two species. The diffusion Monte Carlo method is used to calculate the ground-state energy…
Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…