Manfred Einsiedler, Thomas Ward

eBook, PDF

Ergodic Theory (eBook, PDF)

with a view towards Number Theory

Beschreibung

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 5.17MB

Barrierefreiheit

• Text-to-Speech

Autor

Menny Aka studied at the Hebrew University, with a Ph.D. in 2012 under Alexander Lubotzky. He held research positions at EPFL and ETH Zürich before becoming a senior scientist at ETH Zürich. He works on the interaction between number theory, ergodic theory and group theory. An enthusiastic and innovative lecturer, he is interested in making mathematics accessible, especially to younger audiences. He has initiated and taught in various programs for high school students, including projects aimed at gifted students and prospective undergraduates. He is interested in showcasing the beauty and simplicity underpinning complex mathematical ideas. Manfred Einsiedler studied at the University of Vienna, with a Ph.D. in 1999 under Klaus Schmidt. He held research positions at the University of East Anglia, Penn State University, the University of Washington, and Princeton University as a Clay Research Scholar. After becoming a Professor at Ohio State University he joinedETH Zürich. In 2004 he won the Research Prize of the Austrian Mathematical Society, in 2008 he was an invited speaker at the European Mathematical Congress in Amsterdam, and in 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad. He works on ergodic theory (especially dynamical and equidistribution problems on homogeneous spaces) and its applications to number theory. He has collaborated with Grigory Margulis and Akshay Venkatesh. With Elon Lindenstrauss and Anatole Katok, Einsiedler proved that a conjecture of Littlewood on Diophantine approximation is "almost always" true. Thomas Ward studied at the University of Warwick, with a Ph.D. in 1989 under Klaus Schmidt. He held research positions at the University of Maryland, College Park and at Ohio State University before joining the University of East Anglia in 1992. Since 2008 he has served on university executives, as Pro-Vice-Chancellor for Education at the University of East Anglia and Durham University, and since 2016 as Deputy Vice-Chancellor (Student Education) at the University of Leeds. He worked on the ergodic theory of algebraic dynamical systems, compact group automorphisms, and number theory. A long collaboration with Graham Everest on links between number theory and dynamical systems included the book "Heights of polynomials and entropy in algebraic dynamics" and a paper on Diophantine equations that won the 2012 Lester Ford Prize for mathematical exposition. With Einsiedler he has written "Ergodic theory with a view towards number theory" in 2011 and "Functional analysis, spectral theory, and applications" in 2017.

Produktdetails

• Verlag: Springer London
• Seitenzahl: 481
• Erscheinungstermin: 11. September 2010
• Englisch
• ISBN-13: 9780857290212
• Artikelnr.: 43727896

Rezensionen

From the reviews:

"The book is an introduction to ergodic theory and dynamical systems. ... The book is intended for graduate students and researchers with some background in measure theory and functional analysis. Definitely, it is a book of great interest for researchers in ergodic theory, homogeneous dynamics or number theory." (Antonio Díaz-Cano Ocaña, The European Mathematical Society, January, 2014)

"A book with a wider perspective on ergodic theory, and yet with a focus on the interaction with number theory, remained a glaring need in the overall context of the development of the subject. ... The book under review goes a long way in fulfilling this need. ... it covers a good deal of conventional ground in ergodic

theory ... . a very welcome addition and would no doubt inspire interest in the area among researchers as well as students, and cater to it successfully." (S. G. Dani, Ergodic Theory and Dynamical Systems, Vol. 32 (3), June, 2012)

"The book under review is an introductory textbook on ergodic theory, written with applications to number theory in mind. ... it aims both to provide the reader with a solid comprehensive background in the main results of ergodic theory, and of reaching nontrivial applications to number theory. ... The book should also be very appealing to more advanced readers already conducting research in representation theory or number theory, who are interested in understanding the basis of the recent interaction with ergodic theory." (Barak Weiss, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 114, 2012)

"This introductory book, which goes beyond the standard texts and allows the reader to get a glimpse of modern developments, is a timely and welcome addition to the existing and ever-growing ergodic literature. ... This book is highly recommended to graduate students and indeed to anyone who is interested in acquiring a better understanding of contemporarydevelopments in mathematics." (Vitaly Bergelson, Mathematical Reviews, Issue 2012 d)

"The book contains a presentation of the ergodic theory field, focusing mainly on results applicable to number theory. ... of interest for researchers, specialists, professors and students that work within some other areas than precisely the ergodic theory. ... 'Ergodic Theory. With a view toward number theory' is now an indispensable reference in the domain and offers important instruments of research for other theoretical fields." (Adrian Atanasiu, Zentralblatt MATH, Vol. 1206, 2011)