Is the dimension of chaotic attractors invariant under coordinate changes?

Several different dimensionlike quantities, which have been suggested as being relevant to the study of chaotic attractors, are examined. In particular, we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points. It is found that some are and some are not. It is suggested that the word dimension be reversed only for those quantities have this invariance property.     

Indecomposable continua in dynamical systems with noise: Fluid flow past an array of cylinders

Standard dynamical systems theory is based on the study of invariant sets. However, when noise is added, there are no bounded invariant sets. Our goal is then to study the fractal structure that exists even with noise. The problem we investigate is fluid flow past an array of cylinders. We study a parameter range for which there is a periodic oscillation of the fluid, represented by vortices being shed past each cylinder. Since the motion is periodic in time, we can study a time-1 Poincare map. Then we add a small amount of noise, so that on each iteration the Poincare map is perturbed smoothly, but differently for each time cycle. Fix an x coordinate x(0) and an initial time t(0). We discuss when the set of initial points at a time t(0) whose trajectory (x(t),y(t)) is semibounded (i.e., x(t)>x(0) for all time) has a fractal structure called an indecomposable continuum. We believe that the indecomposable continuum will become a fundamental object in the study of dynamical systems with noise. (c) 1997 American Institute of Physics.     

Metamorphoses: Sudden jumps in basin boundaries

In some invertible maps of the plane that depend on a parameter, boundaries of basins of attraction are extremely sensitive to small changes in the parameter. A basin boundary can jump suddenly, and, as it does, change from being smooth to fractal. Such changes are calledbasin boundary metamorphoses. We prove (under certain non-degeneracy assumptions) that a metamorphosis occurs when the stable and unstable manifolds of a periodic saddle on the boundary undergo a homoclinic tangency.This research was supported in part by grants and contracts from the Defense Advanced Research Projects Agency, the Consiglio Nazionale delle Ricerche (Comitato per le Matematiche), and the National Science Foundation     

Fractal properties of critical invariant curves

We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension.     

Quantitation of nine quinolones in chicken tissues by high-performance liquid chromatography with fluorescence detection

A simple reversed-phase high-performance liquid chromatographic method was developed and validated for simultaneous analysis of nine quinolones (ciprofloxacin, danofloxacin, difloxacin, enrofloxacin, flumequine, marbofloxacin, nalidixic acid, oxolinic acid, sarafloxacin) in chicken tissue. The analytes were extracted from homogenized muscle using an acetonitrile basic solution. After centrifugation and partial evaporation, direct injection was possible. Three different HPLC conditions were applied to quantify the residual quinolones. Separation was achieved on a PLRP-S column and detection was performed with a monochromator fluorescence detector. The recovery, the limit of detection, the limit of quantification, the accuracy and the precision of the method were evaluated from spiked tissue samples at concentration levels ranging from 15 microg kg(-1) to 300 microg kg(-1) according to the maximum residue limit of each quinolone. This method is also suitable for porcine, bovine, ovine and fish muscle tissue.