Geometry of Continued Fractions

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  • Geometry of Continued Fractions Book Detail

  • Author : Oleg Karpenkov
  • Release Date : 2013-08-15
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 409
  • ISBN 13 : 3642393683
  • File Size : 65,65 MB

Geometry of Continued Fractions by Oleg Karpenkov PDF Summary

Book Description: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

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Geometry of Continued Fractions

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Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise

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This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximati

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Continued Fractions consists of two volumes -- Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2