Generalized Notions of Continued Fractions: Ergodicity and Number Theoretic Applications

— —

Juan Fernández Sánchez Jerónimo López-Salazar Codes

Generalized Notions of Continued Fractions

Ergodicity and Number Theoretic Applications

Juan Fernández Sánchez, Jerónimo López-Salazar Codes, Juan B. Seoane Sepúlveda (UCM, Spain) , Wolfgang Trutschnig

$326

Hardback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Chapman & Hall/CRC
20 July 2023

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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

By: Juan Fernández Sánchez, Jerónimo López-Salazar Codes, Juan B. Seoane Sepúlveda (UCM, Spain), Wolfgang Trutschnig
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 449g
ISBN: 9781032516783
ISBN 10: 103251678X
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 142
Publication Date: 20 July 2023
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Juan Fernández Sánchez earned his Ph.D. in mathematics from the University of Almería (Spain) in 2010. His research interests are in dependence modeling and copulas, dynamical systems, singular functions, and number theory. Jerónimo López-Salazar Codes completed his doctoral work under the supervision of Professors José María Martínez Ansemil and Socorro Ponte at Universidad Complutense de Madrid (Spain) and obtained his Ph.D. degree in 2013. He currently works at Universidad Politécnica de Madrid (Spain). His research is mainly devoted to infinite dimensional holomorphy and lineability. Juan B. Seoane Sepúlveda earned his first Ph.D. at the Universidad de Cádiz (Spain) jointly with Universität Karlsruhe (Germany) in 2005. His received his second Ph.D. at Kent State University (Kent, Ohio, USA) in 2006. His main interests include Real and Complex Analysis, Operator Theory, Number Theory, Mathematical Modeling, Mathematical Biology, Geometry of Banach spaces, History of Mathematics, and Lineability. He is the author of over 200 scientific publications, including several books. He is currently a professor at Universidad Complutense de Madrid, where he also holds the position of director of the Master’s in Advanced Mathematics. Wolfgang Trutschnig obtained his Ph.D. at the Vienna University of Technology, Austria, in 2006. He is currently the professor for stochastics and director of the IDA Lab at the Paris Lodron University Salzburg (PLUS) and mainly works in dependence modeling and nonparametric statistics with regular excursions to dynamical systems, fractals and ergodic theory.