Research on the First Musique Concrète: The Case of Xenakis’s First Electroacoustic Pieces

Xenakis’s first electroacoustic pieces (Diamorphoses, 1957; Concret PH, 1958; Analogique B, 1959; Orient-Occident, 1960; and Bohor, 1962) can be called musique concrète. Indeed, these works use the concrète musique tape techniques. But their spirit and aesthetic is very different from those set forth in Pierre Schaeffer’s theories. In fact, these works are quite particular in their whole conception. The two authors of this article are researching this period of Xenakis’s electroacoustic music. In this article, they offer a brief survey of the issues these works raised. To illustrate some of these issues, they use Diamorphoses and Bohor as examples.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.