Related papers: A few things I learnt from Jurgen Moser
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not…
In this expository paper, we provide the readers with an overview of Dennis Sullivan's major contributions to the area of Dynamical Systems.
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
The aim of this report is to review a theoretical approach that has been proposed recently to describe dynamic fluctuations in glassy systems (work in collaboration with H. Castillo, C. Chamon, P. Charbonneau, J. L. Iguain, M. Kennett, D.…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families…
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan School of Geometric Dynamical Systems founded by the author.…
The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an…
Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
We introduce a family of classical integrable systems describing dynamics of $M$ interacting ${\rm gl}_N$ integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the ${\rm GL}_N$…
I know better than to come between the experts here assembled and their research programs, so I confine these remarks to lessons to be drawn on the state of our subject from the histories of research in three Windows on the Universe:…
Several design parameters in collective robotic systems have been investigated and developed in order to explore the cooperation among the autonomous robotic individuals in a variety of robotic swarms in the presence of different internal…
What is a systems approach? The first step towards answering this question is an understanding of the history of the systems movement, which includes a survey of contemporary systems discourse. In particular, I examine how systems…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
This article is a multiauthored portrait of Edsger Wybe Dijkstra that consists of testimonials written by several friends, colleagues, and students of his. It provides unique insights into his personality, working style and habits, and his…