相关论文: Nonexpansive chaotic almost minimal systems on res…
The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
We investigate the dynamics of the quasi-periodic swing equations from the perspective of weak KAM theory. To this end, we firstly study a class of Hamiltonian systems. We obtain that the limit $u$, which derived from convergence of a…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
In discrete schemes, weak KAM solutions may be interpreted as approximations of correctors for some Hamilton-Jacobi equations in the periodic setting. It is known that correctors may not exist in the almost periodic setting. We show the…
In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We…
The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of $\beta \N$, or it is a "tame" topological space whose topology…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…
We consider a class of fully nonlinear Schr\"odinger equations and we prove the existence and the stability of Cantor families of quasi-periodic, small amplitude solutions. We deal with reversible autonomous nonlinearities and we look for…
In this paper we study the problem of the existence of a least-action principle for invertible, second-order dynamical systems, discrete in time and space. We show that, when the configuration space is finite, a least-action principle does…
Families of regimes for control systems are studied possessing the so called quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the degree of transients overshooting…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary…
A group G is almost cyclic if there is an element x in G, such that for all g in G, there is an element y in G and an integer n with ygy^{-1} = x^n (that is, every element is conjugate to some power of x). W. Ziller asked whether there are…