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Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

A fixed point for which the stability matrix has both eigenvalues of the same sign (i.e., both are positive or both are negative). If lambda_1<lambda_2<0, then the node is ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

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 most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

A fixed point which has one zero eigenvector.

A fixed point for which the stability matrix has equal nonzero eigenvectors.

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(0,0) = 0 (1) [(partialf)/(partialx)]_(mu=0,x=0) = -1 (2) [(partial^2f)/(partialx^2)]_(mu=0,x=0) < 0 (3) ...