Quantisations of piecewise affine maps on the torus and their quantum limits

For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the so called quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, and examples of non-ergodic maps where arbitrary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking

Vocal imitations and the identification of sound events

International audienceIt is commonly observed that a speaker vocally imitates a sound that she or he intends to communicate to an interlocutor. We report on an experiment that examined the assumption that vocal imitations can e ffectively communicate a referent sound, and that they do so by conveying the features necessary for the identifi cation of the referent sound event. Subjects were required to sort a set of vocal imitations of everyday sounds. The resulting clusters corresponded in most of the cases to the categories of the referent sound events, indicating that the imitations enabled the listeners to recover what was imitated. Furthermore, a binary decision tree analysis showed that a few characteristic acoustic features predicted the clusters. These features also predicted the classi fication of the referent sounds, but did not generalize to the categorization of other sounds. This showed that, for the speaker, vocally imitating a sound consists of conveying the acoustic features important for recognition, within the constraints of human vocal production. As such vocal imitations prove to be a phenomenon potentially useful to study sound identifi cation

De la valeur primitive des intonations du slave commun

Troubetzkoy N. S. De la valeur primitive des intonations du slave commun. In: Revue des études slaves, tome 1, fascicule 3-4, 1921. pp. 171-187

Essai sur la chronologie de certains faits phonétiques du slave commun

Troubetzkoy N. S. Essai sur la chronologie de certains faits phonétiques du slave commun. In: Revue des études slaves, tome 2, fascicule 3-4, 1922. pp. 217-234

Les voyelles nasales des langues léchites

Troubetzkoy N. S. Les voyelles nasales des langues léchites. In: Revue des études slaves, tome 5, fascicule 1-2, 1925. pp. 24-37

Ergodicity of Billiards in Polygons with Pockets

The billiard in a polygon is not always ergodic and never K-mixing or Bernoulli. Here we consider billiard tables by attaching disks to each vertex of an arbitrary simply connected, convex polygon. We show that the billiard on such a table is ergodic, K-mixing and Bernoulli. 1 Introduction Consider the billiard problem in a polygon. Let P be a polygon in which a particle moves freely and bounces elastically off the boundary @P . Assuming the speed of the particle be unit, the phase space will be TP = P \Theta S 1 . The flow OE t : TP ! TP is called the billiard flow. It preserves the Liouville measure d¯ = dq \Theta dv, where dq and dv are uniform measures on P and S 1 , respectively. All the Lyapunov exponents of the billiard flow in any polygon are zero, its topological entropy [18] and Kolmogorov-Sinai entropy [1, 24] are zero as well. The ergodic properties of the billiard flow depend on the shape of the polygon P . On the one hand, billiards in the so called rational polygons..