Snakes on a Plane | Ghost in the Shell: Stand Alone Complex | Theodore Roosevelt National Wildlife Refuge Complex | plane | Outlands (plane) | The Chimpanzee Complex | Prime Material Plane | Oedipus complex | Meadowlands Sports Complex | Jay Jay the Jet Plane | The Plane Train | Next Plane Out | military-industrial complex | Kennedy Space Center Visitor Complex | Inclined plane | Goldstone Deep Space Communications Complex | complex | Y-12 National Security Complex | William Plane Pycraft | Watergate complex | Mi-2/NuRD complex | Ladd S. Gordon Waterfowl Complex | inclined plane | Faliro Coastal Zone Olympic Complex | Complex (magazine) | Complex | Col de Joux Plane | Athens Olympic Sports Complex | Victory Base Complex | Truman Sports Complex |
For example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane; it is now thought of in terms of finite exponential sums (that is, on the unit circle, but with the power series truncated).
In the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.
The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a path integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953.
Henri Poincaré proved that the map f is essentially unique: if z0 is an element of U and φ is an arbitrary angle, then there exists precisely one f as above such that f(z0) = 0 and that the argument of the derivative of f at the point z0 is equal to φ.
In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane.
The Lindsey–Fox algorithm uses the FFT (fast Fourier transform) to very efficiently conduct a grid search in the complex plane to find accurate approximations to the N roots (zeros) of an Nth-degree polynomial.
For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ℝ.