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A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

A two-dimensional piecewise linear map defined by x_(n+1) = 1-y_n+|x_n| (1) y_(n+1) = x_n. (2) The map is chaotic in the filled region above and stable in the six hexagonal ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

x_(n+1) = 2x_n (1) y_(n+1) = alphay_n+cos(4pix_n), (2) where x_n, y_n are computed mod 1 (Kaplan and Yorke 1979). The Kaplan-Yorke map with alpha=0.2 has correlation exponent ...

A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by x_(n+1)=mu(1-2|x_n-1/2|). (1) The first few iterations of (1) give x_1 ...

A basin of attraction in which every point on the common boundary of that basin and another basin is also a boundary of a third basin. In other words, no matter how closely a ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

Gödel's first incompleteness theorem states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...