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The study of the nature and properties of bifurcations.

A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information ...

Schroeder (1991) calls the ceiling function symbols [ and ] the "gallows" because of their similarity in appearance to the structure used for hangings.

The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

The system of ordinary differential equations X^. = sigma(Y-X) (1) Y^. = rX-Y-XZ (2) Z^. = XY-bZ. (3)

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

A 10-digit number satisfying the following property. Number the digits 0 to 9, and let digit n be the number of ns in the number. There is exactly one such number: 6210001000.

Sinai billiards is the reflection of a ray of light by an arrangement of perfectly reflecting circles in the plane (Trott 2004, pp. 28-30). The path is extremely sensitive to ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...