Related papers: Dennis Sullivan's Work on Dynamics
The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
We give a short appreciation of Robin Milner's seminal contributions to the theory of concurrency.
This article reviews the current status of spin dynamics in semiconductors which has achieved a lot of progress in the past years due to the fast growing field of semiconductor spintronics. The primary focus is the theoretical and…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.
This paper is a survey about recent progress in measure rigidity and global rigidity of Anosov actions, and celebrates the profound contributions by Federico Rodriguez Hertz to rigidity in dynamical systems.
The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra. We include results from the recent literature building on Stanley's work,…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
The symposium has shown the dynamism of this rapidly evolving discipline. I shall concentrate here on some highlights and some complementary informations. I conclude on open questions with some perspectives on solar & stellar activity and…
Studies on the dynamical properties of the $\sigma$ meson are reviewed and discussed. The important role of fundamental principles such as analyticity, unitarity and crossing symmetry played in the studies are stressed.
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
A survey is made of several aspects of the dynamics of networks, with special emphasis on unsupervised learning processes, non-Gaussian data analysis and pattern recognition in networks with complex nodes.