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Experal

Mathematics

Ergodic Theory of Fibred Systems and Metric Number Theory

Sold byBooks for Life

SKU: 9780198534884

S$69.12

Only 10 left in stock

Description

Several questions of metric number theory can be successfully handled by the application of ergodic theory. Such an application is possible if an appropriate dynamical system (called fibred system) can be constructed which displays some nice ergodic properties. In this book the basic notion of a fibred system is considered. Most of these systems are connected with f-expansions i.e. generalizations of decimal expansions and continued fractions. There is ample treatment of multidimensional continued fractions including the recent applications of subadditive ergodic theorems to Diophantine approximation. Next, basic properties like ergodicity, conservativity, and existence of invarient measures are discussed. Here several auxiliary constructions as first return map or jim transformation are useful. As a further basic tool the Ruelle-Frobenius-Perron transfer operator is considered.Table of Content1: Basic definitions. 2: Series expansions. 3: Continued fractions. 4: Algorithms of 'cotangent type'. 5: Unimodal maps and piecewise property E-maps. 6: Multidimensional continued fractions. 7: Maps on the real axis. 8: f-expansions. 9: Ergodicity. 10: Examples of non-ergodic systems. 11: Distribution theorems for Oppenheim series. 12: Invariant measures. 13: Kuzmin's equation. 14: The Parry-Daniels maps. 15: Renyi's condition. 16: Auxiliary measures. 17: First return map. 18: Jump transformations I. 19: Jump transformations II. 20: Invariant measures for maps with indifferent fixed points. 21: Dual algorithms. 22: Piecewise fractional linear maps. 23: Ergodocity and invariant measures for multidimensional continued fractions. 24: Natural extensions and Diophantine problems. 25: The Kuzmin-Frobenius-Perron operator. 26: The case of continued fractions. 27: The Lasota-Yorke approach. 28: Distortion and other functionals. 29: Some more results on the Kuzmin operator. 30: The quadratic map. 31: Exponents of convergence for multidimensional continued fractions. References

Specifications

ISBN-13: 9780198534884
Author: Fritz Schweiger
Publisher: Oxford University Press
Publication Date: 1995-01-01
Binding: hardcover
Condition: new
Pages: 308
Language: english
Country of Origin: United States
Weight (g): 400
Height (mm): 30
Length (mm): 198
Width (mm): 132

Frequently Asked Questions

: Standard shipping to Singapore typically takes 1–2 business days after dispatch. Express options are available at checkout.
: We offer a 30-day return window for most products. Items must be unused, in their original packaging, and accompanied by proof of purchase to qualify for a full refund.
: We accept all major credit and debit cards (Visa, Mastercard, American Express), as well as Apple Pay and Google Pay. All transactions are processed securely via Stripe and charged in SGD.
: Yes — we never store your card details. All payments are handled by Stripe, a PCI-DSS Level 1 certified payment processor, using industry-standard TLS encryption.
: Some products can be backordered — you will see a note on the product page if this is the case. We will ship as soon as stock arrives and keep you updated via email.
: Once your order is dispatched you will receive a shipping confirmation email containing your tracking number and a link to track your parcel in real time.