An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor (see strange attractor below). If the …

In dynamical systems, a 'Strange Attractor' is a type of attractor (a region or shape to which points are 'pulled' as the result of a certain process) that arises in certain non-linear systems and is …

Strange attractors are an extension of iteration to two and three dimensions. The most famous of these is the Lorenz attractor — a mathematical experiment in weather prediction that …

Strange Attractors. Edward Lorenz's first weather model exhibited chaotic behavior, but it involved a set of 12 nonlinear differential equations. Lorenz decided to look for complex behavior in an …

In this lecture we begin our study of strange attractors. We emphasize their generic features. Initital conditions inside or outside the limit cycle always evolve to the limit cycle. ow (i.e., it …

2014年8月18日 · For smooth dynamical systems two types of strange attractors which are preserved by small perturbations have been theoretically studied — attractors which are …

2025年1月20日 · An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly. A …

strange attractor is the Lyapunov dimension D L. It is de ned as the number of ordered Lyapunov exponents that sum to zero. For the attractors listed in the table above, D L becomes 0 for the …

2024年5月21日 · A strange attractor is a concept in chaos theory that is used to describe the behavior of chaotic systems. Unlike a normal attractor, a strange attractor predicts the …

attractor. This set is prototypical of what one wants to call a strange attractor. Such objects often arise when a diffeomorphism f stretches and folds an open set U and maps the closure …