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A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...

The condition for isoenergetic nondegeneracy for a Hamiltonian H=H_0(I)+epsilonH_1(I,theta) is |(partial^2H_0)/(partialI_ipartialI_j) (partialH_0)/(partialI_i); ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

Any of the three standard forms in which an elliptic integral can be expressed.

The sphere with respect to which inverse points are computed (i.e., with respect to which geometrical inversion is performed). For example, the cyclides are inversions in a ...

If s_x is the standard deviation of a set of samples x_i and x^_ their mean, then the variation coefficient is defined as V=(s_x)/(x^_).

gamma_r=(kappa_r)/(sigma^(r+2)), where kappa_r are cumulants and sigma is the standard deviation.

A handlebody of type (n,k) is an n-dimensional manifold that is attained from the standard n-disk by attaching only k-D handles.

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...