Sur les endomorphismes holomorphes permutables de $$\mathbb{P}^k$$

Let , be holomorphic endomorphisms of of degrees , . Assume that and that for all integers , . We then show that are critically finite. Moreover there is an orbifold such that , are coverings of . In the case we give the list of commuting pairs satisfying the above conditions. We also show that any endomorphism is approximable by endomorphisms commuting only with their iterates.

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Sur les endomorphismes holomorphes permutables de $\mathbb{P}^k$

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Received: 6 April 2001 / Published online: 17 June 2002     

Equidistribution of saddle periodic points for Hénon-type automorphisms of $$\mathbb {C}^k$$

In this paper, we prove the equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb {C}^k\) with respect to its equilibrium measure. A general strategy to obtain equidistribution properties in any dimension is presented. It is based on our recent theory of densities for positive closed currents. Several fine properties of dynamical currents are also proved.     

Preparation and evaluation of some novel liquid crystals as antioxidants

Four liquid crystal compounds of the form 2-sec-butyl-4-[(4-X-phenyl) diazenyl) phenyl-4-(octadecyloxy] benzoate symbolized as I18_a, I18_b, I18_c, and I18_d were prepared in which the substituent (X) was taken CH₃O-, CH₃-, Br-, and -NO₂, respectively. Characterization of prepared compounds is done using FT-IR, ¹H-NMR, mass spectroscopy, and elemental analysis. Their mesophase was investigated by differential scanning calorimetry. Their antioxidant efficiency for Egyptian lubricating base oil was tested via monitoring the oxidation reaction through the change in total acid number. The obtained results showed that the efficiency of these compounds was ranked as follows I18_d > I18_c > I18_b > I18_a.     

Surface-active properties of new cationic gemini surfactants with cyclic spacer

Three cationic gemini surface active compounds of the type (1r,4r)-1,4-dialkyl-1,4-dimethy-l-piperazine-1,4-diium bromide (Ia, Ib, and Ic), were synthesized. They were characterized using elemental analysis and ¹H-NMR spectra. Their surface-active properties were measured in aqueous solutions with different concentrations at different temperatures (25, 40, and 55°C). Various surface measurements of these gemini surfactants, (compared to the conventional one, 1-Dodecyl-1-methylpiperidinium bromide (a)) were estimated, specifically critical micelle concentration (CMC), effectiveness (π_CMC), efficiency (P_C20) as well as maximum surface excess (Γ_max) and minimum surface area (A_min). The measurements of the gemini compounds gave low CMC, high efficiency in reducing the surface tension, and intense adsorption at air/water interface. These surfactants have lower Krafft points and thus better solubility. Thermodynamic data, free energy, entropy, and enthalpy changes (ΔG°, ΔS°, and ΔH°) for micellization at the air/water interface and also for adsorption in the bulk of surface-active solutions were calculated.     

Dynamics of polynomial automorphisms ofC k

We study the dynamics of polynomial automorphisms ofC ^k . To an algebraically stable automorphism we associate positive closed currents which are invariant underf, consideringf as a rational map onP ^k . These currents give information on the dynamics and allow us to construct a canonical invariant measure which is shown to be mixing.     

Equidistribution speed for endomorphisms of projective spaces

Let f be a non-invertible holomorphic endomorphism of \mathbbP^k{\mathbb{P}^{k}}, f ⁿ its iterate of order n and μ the equilibrium measure of f. We estimate the speed of convergence in the following known result. If a is a Zariski generic point in \mathbbP^k{\mathbb{P}^{k}}, the probability measures, equidistributed on the preimages of a under f ⁿ , converge to μ as n goes to infinity.     

Ensemble des zéros d'une fonction holomorphe bornée dans la boule unité

Sans résumé     

Upper bound for the topological entropy of a meromorphic correspondence

Let f be a meromorphic correspondence on a compact Kähler manifold. We show that the topological entropy of f is bounded from above by the logarithm of its maximal dynamical degree. An analogous estimate for the entropy on subvarieties is given. We also discuss a notion of Julia and Fatou sets.     

Spectre de A(\̄gW) pour des domaines bornés faiblement pseudoconvexes réguliers

If Ω is a weakly pseudoconvex domain in a Stein manifold, then the spectrum of the Frechet Algebra $\text{A}{}^{\mathrm{\infty }}\text{(}\text{}\text{?}\text{gW)}$ is isomorphic to $\text{}\text{?}\text{gW, A}{}^{\mathrm{\infty }}\text{(}\text{}\text{?}\text{gW)}$ denotes the space of holomorphic functions smooth up to the boundary. The spectrum of the uniform algebra $\text{A(}\text{}\text{?}\text{gW)}$ is also isomorphic to -Ω. As a corollary we prove an approximation theorem for plurisubharmonic functions in $\text{Ω}$ continuous in -Ω.