Bounding extrema over global attractors using polynomial optimisation

Strange attractors are classified by bounding Tori.

There is at present a doubly discrete classification for strange attractors of low dimension, d(L)<3. A branched manifold describes the stretching and squeezing processes that generate the strange attractor, and a basis set of orbits describes the complete set of unstable periodic orbits in the attractor. To this we add a third discrete classification level. Strange attractors are organized by ...

Global Extrema in Traveltime Tomography

Classifying extrema using intervals

We present a straightforward and verified method of deciding whether the point x ∈ R, n > 1, such that ∇f(x) = 0, is the local minimizer, maximizer or just a saddle point of a real-valued function f . The method scales linearly with dimensionality of the problem and never produces false results.

Bounding Polynomial Entanglement Measures for Mixed States

On bounding boxes of iterated function system attractors

Before rendering 2D or 3D fractals with iterated function systems, it is necessary to calculate the bounding extent of fractals. We develop a new algorithm to compute the bounding box which closely contains the entire attractor of an iterated function system. r 2003 Elsevier Science Ltd. All rights reserved.