Generalized Notions of Continued Fractions: Ergodicity and Number Theoretic Applications (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

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Synopsis
Ancient times witnessed the origins of the theory of continued fractions. Throughout time, mathematical geniuses such as Euclid, Aryabhata, Fibonacci, Bombelli, Wallis, Huygens, or Euler have made significant contributions to the development of this famous theory, and it continues to evolve today, especially as a means of linking different areas of mathematics.This book, whose primary audience is graduate students and senior researchers, is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions. After deriving invariant ergodic measures for each of the underlying transformations on [0,1] it is shown that any of the famous formulas, going back to Khintchine and Levy, carry over to more general settings. Complementing these results, the entropy of the transformations is calculated and the natural extensions of the dynamical systems to [0,1]2 are analyzed. Features Suitable for graduate students and senior researchers Written by international senior experts in number theory Contains the basic background, including some elementary results, that the reader may need to know before hand, making it a self-contained volume
Copyright:
2023

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9781000907612
Related ISBNs:
9781032516783, 9781003404064, 9781000907582
Publisher:
CRC Press
Date of Addition:
Copyrighted By:
Juan Fernández Sánchez, Jerónimo López-Salazar Codes, Juan B. Seoane Sepúlveda, Wolfgang Trutschnig
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Science, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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