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Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

An operator U satisfying U^|U = 1 (1) UU^| = 1, (2) where U^| is the adjoint.

A function or transformation f in which f(z) does not overlap z. In modular function theory, a function is called univalent on a subgroup G if it is automorphic under G and ...

An unknown is an independent variable of a function. A function with n independent variables is said to be a function "in," "with," or "of" n unknowns.

A fixed point for which the stability matrix has equal positive eigenvalues.

A fixed point for which the stability matrix has both eigenvalues positive, so lambda_1>lambda_2>0.

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=alpha+/-ibeta (with alpha,beta>0).

A fixed point for which the stability matrix has one zero eigenvector with positive eigenvalue lambda>0.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

The number of poles of an automorphic function in the closure of its fundamental region.