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A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

A measure for which the q-dimension D_q varies with q.

A metric defined by d(z,w)=sup{|ln[(u(z))/(u(w))]|:u in H^+}, where H^+ denotes the positive harmonic functions on a domain. The part metric is invariant under conformal maps ...

A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.

Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...

A generalized conformal mapping.

The fractal-like figure obtained by performing the same iteration as for the Mandelbrot set, but adding a random component R, z_(n+1)=z_n^2+c+R. In the above plot, ...

A variable that may assume only real values.

A method for predicting the onset of widespread chaos.

A definition of a function using a contour integral. Schläfli integrals may be converted into Rodrigues representations.