Optimal decisions over time and strange attractors: an analysis by the Bellman principle

Mutual information, strange attractors, and the optimal estimation of dimension.

Strange attractors

do in biology and is, I think, one of the great ways to do innovative work.... The diversity in the living world is so large, and since everything is connected in some way, let’s find the best one.” Research focused on human and medical application is certainly an important component in neuroscience. But such research tends to dwell more on technological improvements rather than on basic discov...

Dimension of Time in Strange Attractors

In the rendering of strange attractors a number of methods are outlined how the element of time can be used. Time can be represented as the number of times a mapped location is selected or when the location is selected. A variety of coloring schemes based on the concept of time are also discussed. The other aspect time serves is the ability to visually suggest three-dimensional surfaces within ...

Bifurcations and Strange Attractors

We reviews the theory of strange attractors and their bifurcations. All known strange attractors may be subdivided into the following three groups: hyperbolic, pseudo-hyperbolic ones and quasi-attractors. For the first ones the description of bifurcations that lead to the appearance of Smale-Williams solenoids and Anosov-type attractors is given. The definition and the description of the attrac...

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 ...