In particular, the Julia set of z + c1 is locally connected if c1 ∈ [−2, 1/4] and totally disconnected if c1 ∈ R \ [−2, 1/4] (note that [−2, 1/4] is equal to the set of parameters c1 ∈ R for which the critical point c = 0 does not escape to infinity). This answers a question posed by Milnor, see [Mil1]. We should emphasize that if the ω-limit set ω(c) of the critical point c = 0 is not minimal ...

Introduction The following notes provide an introduction to recent work of Branner, Hubbard and Yoccoz on the geometry of polynomial Julia sets. They are an expanded version of lectures given in Stony Brook in Spring 1992. I am indebted to help from the audience. Section 1 describes unpublished work by J.-C. Yoccoz on local connectivity of quadratic Julia sets. It presents only the " easy " par...

Renaud Bastien, 2, 3, 4, ∗ Bruno Moulia, 3 Stéphane Douady, and Tomas Bohr Institut Jean-Pierre Bourgin, UMR1318 INRA-AgroParisTech, 78026 Versailles, France INRA, UMR 547 PIAF, F-63100 Clermont Fd Cedex 01 Clermont Université, Université Blaise Pascal, UMR 547 PIAF, BP 10448, F-63000 Clermont-Ferrand Matière et Systèmes Complexes, Université Paris-Diderot, 10 rue Alice Domont et Léonie Duquet,...

The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena. We suggest here a general method for the calculation of the external arguments of external rays landing at the hyperbolic components root points of the Mandelbrot set. Likewise, we prese...

In the gap topology, unbounded self-adjoint Fredholm operators on a Hilbert space have third homotopy group integers. We realise generator explicitly, using family of Dirac half-line, which arises naturally in Weyl semimetals solid-state physics. A “Fermi gerbe” geometrically encodes how discrete spectral data interpolate between essential gaps. Its non-vanishing Dixmier–Douady invariant protec...

In two previous articles [Douady & Couder (1996a,b)] two iterative systems were defined, based respectively on hypotheses developed by Hofmeister (1868) and Snow & Snow (1952). It was shown that in the latter model all the variety of the spiral, whorled and multijugate patterns observed on botany could be obtained as steady regimes of the iteration. In this third article, several of the charact...

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation, which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes [A...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

“a city can be read through its streets”. stéphane douady, professor of dynamics of out-of-equilibrium systems in paris diderot university began his speech with these words. he continued by explaining the significance of the street structure: “when we think of a city, we first think of the houses. while they can be replaced when destroyed or abandoned, the streets remain stable”. dr. douady’s m...