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- Branch_point abstract "In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point (Ablowitz & Fokas 2003, p. 46). Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept.Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation z = w2 for w as a function of z. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an appropriate sense, is continuous at the origin. This is in contrast to transcendental and logarithmic branch points, that is, points at which a multiple-valued function has nontrivial monodromy and an essential singularity. In geometric function theory, unqualified use of the term branch point typically means the former more restrictive kind: the algebraic branch points. In other areas of complex analysis, the unqualified term may also refer to the more general branch points of transcendental type.".
- Branch_point wikiPageID "483173".
- Branch_point wikiPageRevisionID "598975329".
- Branch_point first "E.D.".
- Branch_point hasPhotoCollection Branch_point.
- Branch_point id "B/b017500".
- Branch_point last "Solomentsev".
- Branch_point title "Branch point".
- Branch_point year "2001".
- Branch_point subject Category:Complex_analysis.
- Branch_point subject Category:Inverse_functions.
- Branch_point type Abstraction100002137.
- Branch_point type Function113783816.
- Branch_point type InverseFunction113784537.
- Branch_point type InverseFunctions.
- Branch_point type MathematicalRelation113783581.
- Branch_point type Relation100031921.
- Branch_point comment "In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point (Ablowitz & Fokas 2003, p. 46).".
- Branch_point label "Branch point".
- Branch_point label "Point de branchement".
- Branch_point label "Punkt rozgałęzienia".
- Branch_point label "Vertakkingspunt".
- Branch_point label "Точка ветвления".
- Branch_point label "分岐点 (数学)".
- Branch_point sameAs Point_de_branchement.
- Branch_point sameAs 分岐点_(数学).
- Branch_point sameAs Vertakkingspunt.
- Branch_point sameAs Punkt_rozgałęzienia.
- Branch_point sameAs m.02fxkj.
- Branch_point sameAs Q2625091.
- Branch_point sameAs Q2625091.
- Branch_point sameAs Branch_point.
- Branch_point wasDerivedFrom Branch_point?oldid=598975329.
- Branch_point isPrimaryTopicOf Branch_point.