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An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

"At least one" is a mathematical term meaning one or more. It is commonly used in situations where existence can be established but it is not known how to determine the total ...

An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

The nth root of the content of the set sum of two sets in n-dimensional Euclidean space is greater than or equal to the sum of the nth roots of the contents of the individual ...

The fractal-like two-dimensional function f(x,y)=((x^2-y^2)sin((x+y)/a))/(x^2+y^2). The function is named for the appearance of a butterfly-like pattern centered around the ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...