Jacques Peyrière

• University of Paris-Saclay

Horowitz [2] defined a mapping from a free group Γ of rank n into a quotient ring R of a ring of polynomials on ℤ with 2n - 1 variables in such a way that the value of this mapping (a Fricke character) at a point w in Γ allows to compute the value at w of the character of any representation of Γ in SL(2, ℂ). He also showed [3] that an endomorphism...

This paper defines and studies a general algorithm for constructing new families of fractals in Euclidean space. This algorithm involves a sequence of linear interscale transformations that proceed from large to small scales. The authors find that the fractals obtained in this fashion decompose in intrinsic fashion into linear combinations of a var...

In several problems arising in the quasicrystal theory one is faced with the problem of computing as simply as possible the traces of matrices defined by recursion using a substitution scheme. To be more specific, let us take an example.

Let {λ j } j≥0 be a sequence of positive integers such that λ j+1 /λ j ≥3 and {a j } j≥0 a sequence of complex numbers such that |a j |≤1. Let μ be the Riesz product ∏ j≥0 [1+Re(a j e iλ j x )], that is, the weak limit of measures on T the density of which are the partial products. Then if ∑ j≥0 |α j | 2 <∞, the series ∑ j≥0 α j (e iλ j x -1 2a ¯ j...

The electrical response of porous electrodes is calculated in several particular cases, which permit one to approach the response of a realistic model for a porous interface. The case of nonblocking surfaces and the case of the diffusion impedance of a fractal electrode are also considered. The use of Bode diagrams is shown to provide a very simple...

It is shown that the CPA behavior Z∞ (iω)−η with η=3−D which exists for a blocking “finite modified Sierpinski electrode” when D<5/2, also exists for a non-blocking surface but in a more restricted frequency range. We show also that there exists in series with the electrolyte resistance an effective resistance which depends on the fractal dimension...

Let $p$ be a polynomial function from ${\bf R}^m$ to ${\bf R}$. The lifting of the Lebesgue measure on ${\bf R}^m$ to the graph of $p$ is denoted $\mu _p$. This paper is devoted to the estimation of $\hat{\mu }_p(u,v)$ when $v$ approaches 0 (such distributions $\hat{\mu }_p$ appears as characters of representations of nilpotent Lie groups). Result...