For the family of exponential maps z 7→ exp(z) + κ, we show the following analog of a theorem of Douady and Hubbard concerning polynomials. Suppose that g is a periodic external ray of an exponential map with nonescaping singular value. Then g lands at a repelling or parabolic periodic point. We also show that there are periodic external rays landing at all periodic points of such an exponentia...

We studied the rational realization problem for sub-hyperbolic semi-rational branched coverings. By using the shielding ring lemma, we are able to give a direct proof of CJS’s Theorem following the lines of the proof of Thurston’s Theorem given in the paper of Douady-Hubbard.

In this paper, we study rational functions of the form [Formula: see text] with fixed and at least text], hold either or while other varies. We locate some homeomorphic copies Mandelbrot set in text]-parameter plane for certain ranges as well text]-plane text]-ranges. use techniques first introduced by Douady Hubbard [1985] that were applied subfamily Devaney [2006]. These involve polynomial-li...

Using groupoid S-central extensions, we present, for a compact simple Lie group G, an infinite dimensional model of S-gerbe over the differential stack G/G whose Dixmier-Douady class corresponds to the canonical generator of the equivariant cohomology H G(G). c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Gerbes Equivariantes sur les groupes de Lie simples compa...

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system...

It is shown that if X is an Inoue surface of type SM then the irreducible components of the Douady space of Xn are compact, for all n ≥ 0. This gives an example, asked for in [15], of an essentially saturated compact complex manifold (in the sense of model theory) that is not of Kähler-type. Among the known compact complex surfaces without curves, these are the only examples.

We study the geometry and topology of (filtered) algebra-bundles ΨZ over a smooth manifold X with typical fibre ΨZ(Z;V ), the algebra of classical pseudodifferential operators of integral order on the compact manifold Z acting on smooth sections of a vector bundle V . First a theorem of Duistermaat and Singer is generalized to the assertion that the group of projective invertible Fourier integr...