On some coding and mixing properties for a class of chaotic systems

We study certain ergodic properties of equilibrium measures of hyperbolic non-invertible maps f on basic sets with overlaps Λ. We prove that if the equilibrium measure of a Holder potential , is 1-sided Bernoulli, then f is expanding from the point of view of a pointwise section dimension of . If the measure of maximal entropy μ ₀ is 1-sided Bernoulli, then f is shown to be distance expanding on Λ; and if is 1-sided Bernoulli for f expanding, then must be the measure of maximal entropy. These properties are very different from the case of hyperbolic diffeomorphisms. Another result is about the non 1-sided Bernoullicity for certain equilibrium measures for hyperbolic toral endomorphisms. We also prove the non-existence of generating Rokhlin partitions for measure-preserving endomorphisms in several cases, among which the case of hyperbolic non-expanding toral endomorphisms with Haar measure. Nevertheless the system is shown to have always exponential decay of correlations on Holder observables and to be mixing of any order.     

On some coding and mixing properties for a class of chaotic systems

We study certain ergodic properties of equilibrium measures of hyperbolic non-invertible maps f on basic sets with overlaps Λ. We prove that if the equilibrium measure \({\mu_\phi}\) of a Holder potential \({\phi}\) , is 1-sided Bernoulli, then f is expanding from the point of view of a pointwise section dimension of \({\mu_\phi}\) . If the measure of maximal entropy μ ₀ is 1-sided Bernoulli, then f is shown to be distance expanding on Λ; and if \({\mu_\phi}\) is 1-sided Bernoulli for f expanding, then \({\mu_\phi}\) must be the measure of maximal entropy. These properties are very different from the case of hyperbolic diffeomorphisms. Another result is about the non 1-sided Bernoullicity for certain equilibrium measures for hyperbolic toral endomorphisms. We also prove the non-existence of generating Rokhlin partitions for measure-preserving endomorphisms in several cases, among which the case of hyperbolic non-expanding toral endomorphisms with Haar measure. Nevertheless the system \({(\Lambda, f, \mu_\phi)}\) is shown to have always exponential decay of correlations on Holder observables and to be mixing of any order.     

Au cluster growth on ZnO thin films by pulsed laser deposition

Nanostructures formed by Au nanoparticles on ZnO thin film surface are of interest for applications which include medical implants, gas-sensors, and catalytic systems. A frequency tripled Nd:YAG laser (λ = 355 nm, τ_FWHM ∼ 10 ns) was used for the successive irradiation of the Zn and Au targets. The ZnO films were synthesized in 20 Pa oxygen pressure while the subsequent Au coverage was grown in vacuum. The obtained structures surface morphology, crystalline quality, and chemical composition depth profile were investigated by acoustic (dynamic) mode atomic force microscopy, X-ray diffraction, and wavelength dispersive X-ray spectroscopy. The surface is characterized by a granular morphology, with average grain diameters of a few tens of nanometers. The surface roughness decreases with the increase of the number of laser pulses applied for the irradiation of the Au target. The Au coverage reveals a predominant (1 1 1) texture, whereas the underlying ZnO films are c-axis oriented. A linear dependence was established between the thickness of the Au coverage and the number of laser pulses applied for the irradiation of the Au target.     

Nanoscopic photodeposited structures analyzed by an evanescent optical method

The evanescent field propagating in waveguides was used to evaluate the profile and growth rate of laser photodeposited a-Se. A pulsed KrF excimer laser was used for deposition. The differential-evanescent light leaking image, was used to analyze the nanostructures in the deposited zones. The relation between the emerging light intensity of the evanescent wave and the optical light intensity propagating in the waveguide was connected to an effective range of the evanescent wave leaking power into the deposited material. The technique provides the nanometric profiles of the ultra-thin photodeposited structures.     

Local Geometry and Dynamical Behavior on Folded Basic Sets

We study new phenomena associated with the dynamics of higher dimensional non-invertible, hyperbolic maps f on basic sets of saddle type; the dynamics in this case presents important differences from the case of diffeomorphisms or expanding maps. We show that the stable dimension (i.e. the Hausdorff dimension of the intersection between local stable manifolds and the basic set) and the unstable dimension (similar definition) give a lot of information about the dynamical/ergodic properties of endomorphisms on folded basic sets. We prove a geometric flattening phenomenon associated to the stable dimension, i.e. we show that if the stable dimension is zero at a point, then the fractal Λ must be contained in a submanifold and f is expanding on Λ. We characterize folded attractors and folded repellers, as those basic sets with full unstable dimension, respectively with full stable dimension. We classify possible dynamical behaviors, and establish when is the system (Λ,f,μ) 1-sided or 2-sided Bernoulli for certain equilibrium measures μ on folded basic sets, for a class of perturbation maps.     

Holographic testing of fluorescent photosensitive glass-ceramics

In this paper we investigate the holographic recording properties of the fluorescent photosensitive glass-ceramics. The materials described here, stable up to 400 °C, represent a substantial advancement in the development of long lifetime media for holographic data storage. A detailed physical-chemical characterization of the proposed material is presented. It is shown that volume holograms were obtained after the recording process using a continuum high power laser in an off-axis setup.     

Synthesis of ZnO thin films by 40 ps @ 532 nm laser pulses

The synthesis by pulsed laser deposition of ZnO thin films with a Nd:YAG laser system delivering pulses of 40 ps @ 532 nm is reported. The laser beam irradiated the target placed inside a vacuum chamber evacuated down to 1.33×10⁻¹ Pa. The incident laser fluence was of 28 J/cm² in a spot of 0.1 mm². The ablated material was collected onto double face polished (111) Si or quartz wafers placed parallel at a separation distance of 7 mm. The AFM, SEM, UV-Vis, FT-IR and absorption ellipsometry results indicated that we obtained pure ZnO films with a rather uniform surface, having an average roughness of 37 nm. We observed by SEM that particulates are present on ZnO film surface or embedded into bulk. Their density and dimension were intermediary between particulates observed on similar structures deposited with fs or ns laser pulses. We noticed that the density of the particulates is increasing while their average size is decreasing when passing from ns to ps and fs laser pulses. The average transmission in the UV-Vis spectral region was found to be higher than 85%.     

Equilibrium measures on saddle sets of holomorphic maps on \mathbb{P }^2

We consider the case of hyperbolic basic sets $\Lambda $ of saddle type for holomorphic maps $f:{\mathbb{P }}^2{\mathbb{C }}\rightarrow {\mathbb{P }}^2{\mathbb{C }}$ . We study equilibrium measures $\mu _\phi $ associated to a class of Hölder potentials $\phi $ on $\Lambda $ , and find the measures $\mu _\phi $ of iterates of arbitrary Bowen balls. Estimates for the pointwise dimension $\delta _{\mu _\phi }$ of $\mu _\phi $ that involve Lyapunov exponents and a correction term are found, and also a formula for the Hausdorff dimension of $\mu _\phi $ in the case when the preimage counting function is constant on $\Lambda $ . For terminal/minimal saddle sets we prove that an invariant measure $\nu $ obtained as a wedge product of two positive closed currents, is in fact the measure of maximal entropy for the restriction $f|_\Lambda $ . This allows then to obtain formulas for the measure $\nu $ of arbitrary balls, and to give a formula for the pointwise dimension and the Hausdorff dimension of $\nu $ .     

Spectroscopic study of laser irradiated chromatin

Antiprotonic helium is a metastable three-body neutral atom consisting of an antiproton, a helium nucleus and an electron, which we serendipitously discovered some 20 years ago. The antiproton, which normally annihilates within a few picoseconds when injected into matter, can be “stored” in this system for up to several microseconds, and laser spectroscopy is possible within this time window. From the laser transition frequency, the antiproton-to-electron mass ratio can be deduced to high precision. Recent progress at CERN’s antiproton decelerator (AD) will be discussed.