Related papers: Dynamical systems, simulation, abstract computatio…

We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…

We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theory and harmonic analysis, like the classical Cesaro average…

We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…

Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…

A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether…

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…

The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T.…

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…

We prove almost sure ergodic theorems for a class of systems called quasistatic dynamical systems. These results are needed, because the usual theorem due to Birkhoff does not apply in the absence of invariant measures. We also introduce…

We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…

We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…

Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…

A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…

Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…

We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…