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An alternative name for an associated Legendre polynomial.

The Fibonacci chain map is defined as x_(n+1) = -1/(x_n+epsilon+alphasgn[frac(n(phi-1))-(phi-1)]) (1) phi_(n+1) = frac(phi_n+phi-1), (2) where frac(x) is the fractional part, ...

The partial differential equation u_t=Du_(xx)+u-u^2.

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)

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 flat norm on a current is defined by F(S)=int{Area T+Vol(R):S-T=partialR}, where partialR is the boundary of R.

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

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) ...

An action with G=R. Flows are generated by vector fields and vice versa.

A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.