Expressive timing is vital for the aesthetic quality that makes us appreciate performed music. It is a largely tacit skill that musicians acquire by practice. A long-standing intuition is that expressive timing is closely related to the concept of motion. This view leads naturally to the adoption of a dynamical systems approach to the study of expressive timing. A well-known visualization techn...

Cognitive systems are wilder than today's dynamical systems theory can handle. While cognitive systems might be tamed in principle, it seems that the very notion of a dynamical system will change in the process.

This article surveys some recent applications of ideas from dynamical systems theory to understand the qualitative behavior of solutions of dissipative partial differential equations with a particular emphasis on the two-dimensional Navier-Stokes equations.

We solve a problem by V. I. Arnold dealing with “how random” modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form in the case of arithmetic progressions. This simplified expression is then estimated using the methodology of dynamical analysis, which operat...

Given a factor code π from a shift of finite type X onto a sofic shift Y , the class degree of π is defined to be the minimal number of transition classes over the points of Y . In this paper, we investigate the structure of transition classes and present several dynamical properties analogous to the properties of fibers of finite-to-one factor codes. As a corollary, we show that for an irreduc...

We give an introduction to a recent direction of research in set theory, developed primarily over the last 15–20 years, and discuss its connections with aspects of dynamical systems and in particular rigidity phenomena in the context of ergodic theory.

Readers of the current issue will find something unfamiliar , perhaps tantalizing, perhaps unsettling. I am referring to the articles by Cha et al. (see " Ionic mechanisms and Ca 2+ dynamics... " and " Time-dependent changes in membrane excitability... "). The first of these articles is less exotic; it presents computer simulations of a model for bursting electrical activity in pancreatic  cel...

We construct templates for geodesic flows on an infinite family of Hecke triangle groups. Our results generalize those of E. Ghys [Knots and dynamics. Proc. Int. Congress of Mathematicians. Vol. 1. International Congress of Mathematicians, Zürich, 2007], who constructed a template for the modular flow in the complement of the trefoil knot in S3. A significant difficulty that arises in any attem...

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

Reacting flow fields are often subject to unsteadiness due flow, reaction, diffusion, and acoustics. Further, flames can also exhibit inherent caused by various intrinsic instabilities. Interaction between unsteady processes across multiple scales makes combustion dynamics complex. Characterizing such complex is essential ensure the safe reliable operation of high efficiency systems. Tools from...