Linked from

The 37 pages that link to Fixed point, each with the reason it gives.

• Dynamical systemBroader topic: In a dynamical system, fixed points are states that do not evolve.

• SymmetryRelated: Rotations and reflections often reveal their structure through the points they leave fixed.

• Brouwer fixed-point theoremBroader topic: The theorem guarantees at least one such point for every map meeting its hypotheses.

• Fixed-point theoremBroader topic: It is the object whose existence every fixed-point theorem concerns.

• Banach fixed-point theoremNarrower topic: The theorem guarantees existence and uniqueness of this kind of point.

• Invariant (mathematics)Related: A fixed point is a special case where the object itself, not merely a property, is preserved.

• Nonlinear systemRelated: Fixed points identify steady states of nonlinear transformations.

• Poincaré mapRelated: A fixed point represents a trajectory returning to the same section point after one circuit.

• Möbius transformationRelated: Solving the Möbius fixed-point equation reveals whether its dynamics are elliptic, parabolic, or loxodromic.

• Symmetry groupRelated: Fixed points help distinguish transformations and characterize stabilizers.

• Rotational symmetryRelated: The center of a planar symmetry rotation is fixed throughout the motion.

• Diagonal lemmaRelated: The lemma produces a sentence whose code behaves like a fixed point of substitution.

• Fixed-point iterationNarrower topic: The iteration seeks a value unchanged by the chosen map.

• L. E. J. BrouwerNarrower topic: The theorem named for Brouwer guarantees such an input under specific topological conditions.

• Nonlinear dynamicsRelated: Fixed points anchor stability analysis and organize nearby trajectories.

• Recursive definitionRelated: Some recursive equations characterize their defined objects as fixed points.

• BifurcationRelated: Fixed points are the discrete-time counterparts of equilibria and can change stability at bifurcations.

• Burnside's lemmaBroader topic: Each group element contributes its number of fixed points to the average.

• Self-referenceRelated: Self-referential constructions often seek a sentence unchanged by a transformation of its description.

• Iterative methodRelated: Many iterative procedures seek a state unchanged by the update rule.

• Scale invarianceRelated: A scale transformation's fixed point represents a description unchanged by rescaling.

• Complex dynamicsBroader topic: Fixed points anchor orbits and are classified by the behavior of nearby iterates.

• Kakutani fixed-point theoremBroader topic: The theorem guarantees exactly this self-membership for at least one point.

• Graph automorphismRelated: A vertex fixed by an automorphism remains in place while other vertices may move.

• Schauder fixed-point theoremBroader topic: The theorem guarantees at least one such point for the specified self-maps.

• Zero of a functionRelated: Fixed points can be found as zeros of the function x ↦ f(x) − x.

• Constant (mathematics)Compared with: A fixed point is a special input-output match, not a value fixed across a function.

• Constant functionCompared with: A constant function has a fixed point only when its fixed output is itself an allowed input.

• Dynamical systems theoryBroader topic: Equilibria are fixed points of a system's time-evolution rule.

• Lefschetz fixed-point theoremBroader topic: The theorem's conclusion is the existence of such a point.

• Pólya enumeration theoremRelated: Burnside’s averaging step counts configurations fixed by each symmetry.

• Daniel Gabriel FahrenheitRelated: Fahrenheit used reference conditions to make thermometer readings comparable.

• Euler's rotation theoremRelated: The fixed point is where the theorem's equivalent rotation axis passes through.

• Edge of chaosCompared with: Fixed points represent a limiting form of orderly behavior.

• Poincaré–Birkhoff theoremBroader topic: The theorem guarantees at least two such points for the specified annulus map.

• Caristi fixed-point theoremNarrower topic: The limiting point is shown to have zero displacement, hence to be fixed.

• Hartman–Grobman theoremNarrower topic: The theorem studies trajectories near a state where the system does not move.