Related papers: A few things I learnt from Jurgen Moser

We analyze a known version of the discrete Wigner function and some connections with Quantum Iterated Funcion Systems. This paper is a follow up of "A dynamical point of view of Quantum Information: entropy and pressure" by the same…

This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…

We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…

It is shown that spin Calogero-Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less then half of the dimension of the phase space. It is also shown that rational spin…

Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…

In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how…

Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…

Ergodic systems, being indecomposable are important part of the study of dynamical systems but if a system is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the…

Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…

In this note, we investigate some topological properties of probabilistic modular spaces.

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main…

Rejoinder: Expert Elicitation for Reliable System Design [arXiv:0708.0279]

This is an introduction to the algebraic aspect of Teichm\"uller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

I will share with the reader what I have learned from Richard Stanley and the ways in which he has contributed to research in combinatorics conducted by me and my collaborators.

We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…

It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…