Isotopy Stable Dynamics Relative to Compact Invariant Sets

Let f be an orientation-preserving homeomorphism of a compactorientable manifold. Sufficient conditions are given for thepersistence of a collection of periodic points under isotopyof f relative to a compact invariant set A. Two main applicationsare described. In the first, A is the closure of a single discreteorbit of f, and f has a Smale horseshoe, all of whose periodicorbits persist; in the second, A is a minimal invariant Cantorset obtained as the limit of a sequence of nested periodic orbits,all of which are shown to persist under isotopy relative toA. 1991 Mathematics Subject Classification: 58F20, 58F15.     

Some properties of a simple moving average when applied to forecasting a time series

Simple (equally weighted) moving averages are frequently used to estimate the current level of a time series, with this value being projected as a forecast for future observations. A key measure of the effectiveness of the method is the sampling error of the estimator, which this paper defines in terms of characteristics of the data. This enables the optimal length of the average for any steady state model to be established and the lead time forecast error derived. A comparison of the performance of a simple moving average (SMA) with an exponentially weighted moving average (EWMA) is made. It is shown that, for a steady state model, the variance of the forecast error is typically less than 3% higher than the appropriate EWMA. This relatively small difference may explain the inconclusive results from the empirical studies about the relative predictive performance of the two methods.     

Broadly tunable single-frequency cw mid-infrared source with milliwatt-level output based on difference-frequency generation in orientation-patterned GaAs

A narrow-linewidth mid-IR source based on difference-frequency generation of an amplified 1.5 microm diode laser and a cw Tm-doped fiber laser in orientation-patterned (OP) GaAs has been developed and evaluated for spectroscopic applications. The source can be tuned to any frequency in the 7.6-8.2 microm range with an output power of 0.5 mW. The measured characteristics of the OP-GaAs sample demonstrate a high quality of the material.     

Compact fiber laser at L-band region using Erbium-doped Zirconia fiber

A compact Erbium-doped fiber laser (EDFL) operating in L-band region is demonstrated using a fabricated Erbium-doped Zirconia fiber (EDZF) for the first time. The fiber is fabricated by combining Zr and Al to achieve the maximum Erbium ion concentration of 4320 wt ppm. By using a fiber Bragg grating (FBG) in a ring configuration, the laser operates at 1579.6 nm with a slope efficiency of 13.6% and the threshold pump power of 25.1 mW. The lasing wavelength is obtained at Bragg wavelength with an output power of 13 dBm and a 3 dB spectral width of 0.02 nm using a piece of 2 m long EDZF in conjunction with 120 mW of 1480 nm pump power.     

High-power Tm-doped fiber distributed-feedback laser at 1943 nm

We report on high-power operation of a fiber distributed-feedback (DFB) laser fabricated from Tm-doped photosensitive alumino-silicate fiber and in-band pumped by an Er/Yb fiber laser at 1565 nm. The fiber DFB laser yielded up to 875 mW of single-ended output at 1943 nm on two orthogonally polarized modes for 3.5 W of absorbed pump power. Further scaling of the DFB laser output power was achieved with the aid of a simple Tm-doped fiber amplifier stage spliced directly to the DFB fiber without the need of an optical isolator. The maximum output power from the DFB laser and fiber amplifier was >3 W for a combined absorbed pump power of 8.1 W. The influence of thermal loading, owing to quantum defect heating in the Tm-doped core, on the output power and longitudinal mode behavior is discussed, and the prospects for further improvement in performance are considered.     

Bifurcations of circle maps: Arnol'd tongues,bistability and rotation intervals

We study the bifurcations of two parameter families of circle maps that are similar tof _b,w (x)=x+w+(b/2) sin (2x) (mod1). The bifurcation diagram is constructed in terms of setsT _r , whereT _r is the set of parameter values (b, w) for whichf _{b, w} has an orbit with rotation numberr. We show that the known structure whenb<1 (forr rational,T _r is an Arnol'd tongue and forr irrational, it is an arc) extends nicely into the regionb>1, wheref _{b, w} is no longer injective and can have an interval of rotation numbers. Specifically, the tongues overlap in a uniform, monotonic manner and forr irrational,T _r opens into a tongue. Our other theorems give information about the dynamics off _{b, w} (e.g., bistability or aperiodicity) for (b, w) in various subsets of parameter space.     

Semiconjugacies to angle-doubling

A simple consequence of a theorem of Franks says that whenever a continuous map, , is homotopic to angle-doubling on the circle, it is semiconjugate to it. We show that when this semiconjugacy has one disconnected point inverse, then the typical point in the circle has a point inverse with uncountably many connected components. Further, in this case the topological entropy of is strictly larger than that of angle-doubling, and the semiconjugacy has unbounded variation. An analogous theorem holds for degree- circle maps with .

     

Photodarkening in Yb-doped aluminosilicate fibers induced by 488 nm irradiation

Photodarkening of Yb-doped aluminosilicate fibers by continuous wave 488 nm irradiation was investigated. The irradiation induced significant excess loss in the UV-visible spectroscopy (VIS) region in Yb-doped aluminosilicate fibers while pure aluminosilicate fibers showed negligible induced loss. Ultraviolet-VIS-near-infrared spectroscopy revealed an absorption peak at 220 nm in unexposed Yb-doped aluminosilicate fiber preforms. The observed peak was attributed to Yb-associated oxygen deficiency centers (ODCs) and proposed as a precursor of the photodarkening. The proposed model was supported by measurements on oxygen-loaded Yb-doped aluminosilicate fibers. In these, the photodarkening could be significantly reduced, which we attribute to a smaller number of ODCs following oxygen loading.