|Forlag||World Scientific Publishing Co|
|Emne||Mathematics; Number theory|
|Se flere detaljer|
Om Continued Fractions
The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.Contents:Generalizations of the gcd and the Euclidean AlgorithmContinued Fractions with Small Partial QuotientsErgodic TheoryComplex Continued FractionsMultidimensional Diophantine ApproximationPowers of an Algebraic IntegerMarshall Hall's TheoremFunctional-Analytic TechniquesThe Generating Function MethodConformal Iterated Function SystemsConvergence of Continued FractionsReadership: Graduate students and researchers in pure and applied mathematics.