Euclidean dynamics | Zendy

Brigitte Vallée | Zendy

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Euclidean dynamics

Author(s) -

Brigitte Vallée

Publication year - 2006

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.15.281

Subject(s) - euclidean geometry , dynamical systems theory , mathematics , dirichlet distribution , class (philosophy) , divisor (algebraic geometry) , euclidean domain , distribution (mathematics) , dynamics (music) , dirichlet series , pure mathematics , discrete mathematics , computer science , euclidean distance matrix , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , acoustics , boundary value problem

We study a general class of Euclidean algorithms which compute the greatest common divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various tools of analytic combinatorics: generating functions, Dirichlet series, Tauberian theorems, Perron’s formula and quasi-powers theorems. Such dynamical analyses can be used to perform the average-case analysis of algorithms, but also (dynamical) analysis in distribution.

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