"Fixed point" has many meanings in science, most of them mathematical.
- Fixed point (mathematics)
- Fixed-point iteration, a general method to compute the fixed point of an iterated function.
- Fixed-point combinator
- For "Fixed-point join" in databases, see Recursive join
- Fixed-point arithmetic, a manner of doing arithmetic on computers
- Benchmark (surveying), fixed points used by geodesists
- For “fixed points” in physics, see Renormalization group
- Fixed points are necessary for a watercraft to be moored to a quay.
- Archimedes said δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω, which is sometimes translated as “Give me a fixed point and I will move the world.”
... bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other ... Another name is blue skies bifurcation in reference to the sudden creation of two fixed points ... If there are two equilibrium points, a stable equilibrium point at and an unstable one at ...
... f R → R be a continuously differentiable function with a fixed point a, f(a) = a ... Consider the dynamical system obtained by iterating the function f The fixed point a is stable if the absolute value of the derivative of f at a is strictly less than 1, and unstable if it is strictly greater than 1 ... This is because near the point a, the function f has a linear approximation with slope f′(a) Thus which means that the derivative measures the rate at which the successive iterates ...
... is equal to zero for some orbit not including the equilibrium point, then that orbit is a stable attractor, but it must be either a limit cycle or n-t ... If the derivative is less than zero everywhere except the equilibrium point, then the equilibrium point is a stable fixed point attractor ... When searching a dynamical system for non-fixed point attractors, the existence of a Lyapunov function can help eliminate regions of parameter space where these dynamics ...
... Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski's undefinability theorem Tarski–Seidenberg theorem Some fixed point theorems, usually variants of the Kleene fixed-p ...
Famous quotes containing the words point and/or fixed:
“How oft when men are at the point of death
Have they been merry! which their keepers call
A lightning before death: O, how may I
Call this a lightning? O my love! my wife!
Death, that hath sucked the honey of thy breath,
Hath had no power yet upon thy beauty:
Thou art not conquered; beautys ensign yet
Is crimson in thy lips and in thy cheeks,
And deaths pale flag is not advanced there.”
—William Shakespeare (15641616)
“It is not merely the likeness which is precious ... but the association and the sense of nearness involved in the thing ... the fact of the very shadow of the person lying there fixed forever! It is the very sanctification of portraits I thinkand it is not at all monstrous in me to say ... that I would rather have such a memorial of one I dearly loved, than the noblest Artists work ever produced.”
—Elizabeth Barrett Browning (18061861)