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A point where a stable and an unstable separatrix (invariant manifold) from the same fixed point or same family intersect. Therefore, the limits lim_(k->infty)f^k(X) and ...

Refer to the above figures. Let X be the point of intersection, with X^' ahead of X on one manifold and X^('') ahead of X of the other. The mapping of each of these points ...

A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

By analogy with the lemniscate functions, hyperbolic lemniscate functions can also be defined arcsinhlemnx = int_0^x(1+t^4)^(1/2)dt (1) = x_2F_1(-1/2,1/4;5/4;-x^4) (2) ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...