What does branch point mean?

Definitions for branch point
branch point

This dictionary definitions page includes all the possible meanings, example usage and translations of the word branch point.

Wikidata

  1. Branch point

    In the mathematical field of complex analysis, a branch point of a multi-valued function is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point. 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of branch point in Chaldean Numerology is: 7

  2. Pythagorean Numerology

    The numerical value of branch point in Pythagorean Numerology is: 3

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"branch point." Definitions.net. STANDS4 LLC, 2024. Web. 27 May 2024. <https://www.definitions.net/definition/branch+point>.

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