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A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

A morphism is a map between two objects in an abstract category. 1. A general morphism is called a homomorphism, 2. A morphism f:Y->X in a category is a monomorphism if, for ...

A point x in a manifold M is said to be nonwandering if, for every open neighborhood U of x, it is true that phi^nU intersection U!=emptyset for a map phi for some n>0. In ...

A quadratic recurrence is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a second-degree polynomial in x_k with k<n. For example, x_n=x_(n-1)x_(n-2) ...

The quotient space X/∼ of a topological space X and an equivalence relation ∼ on X is the set of equivalence classes of points in X (under the equivalence relation ∼) ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...

A strong pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, the map v_m|->g_m(v_m,·) is an ...

A submersion is a smooth map f:M->N when dimM>=dimN, given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the ...