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The Hénon-Heiles equation is a nonlinear nonintegrable Hamiltonian system with x^.. = -(partialV)/(partialx) (1) y^.. = -(partialV)/(partialy), (2) where the potential energy ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

Ai(z) and Ai^'(z) have zeros on the negative real axis only. Bi(z) and Bi^'(z) have zeros on the negative real axis and in the sector pi/3<|argz|<pi/2. The nth (real) roots ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A (Courant and Hilbert 1989, p. 9), i.e., ...

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

A (2n)×(2n) complex matrix A in C^(2n×2n) is said to be Hamiltonian if J_nA=(J_nA)^(H), (1) where J_n in R^(2n×2n) is the matrix of the form J_n=[0 I_n; I_n 0], (2) I_n is ...