Periodicities in Nonlinear Difference Equations

E.A. (University of Rhode Island Grove

ISBN 10: 0849331560 / ISBN 13: 9780849331565

Published by Taylor & Francis Ltd Dez 2004, 2004

About this Item

Neuware - During the last ten years there has been a fascination with discovering nonlinear difference equations of order greater than one. Periodicities in Nonlinear Difference Equations presents in detail the rich periodic character of these equations and brings to the attention of the mathematical community some thought provoking questions, open problems and conjectures worthy of investigation. It also investigates the global character of solutions of these equations for other values of their parameters and attempts to see a more complete picture of the global behavior of their solutions. A comprehensive monograph on the subject, this book can also be used as a supplement for a course on difference equations.

Seller Inventory # 9780849331565

Bibliographic Details

• Title: Periodicities in Nonlinear Difference Equations
• Publisher: Taylor & Francis Ltd Dez 2004
• Publication Date: 2004
• Language: English
• ISBN 10: 0849331560
• ISBN 13: 9780849331565
• Binding: Buch
• Condition: Neu
• Dimensions: 234W x 156H x 0D millimeters 234 millimeters width by 156 millimeters height by 0 millimeters depth
• Weight: 694 grams

About this title

Synopsis

Sharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations. During the last ten years, the authors of this book have been fascinated with discovering periodicities in equations of higher order which for certain values of their parameters have one of the following characteristics: 1. Every solution of the equation is periodic with the same period. 2. Every solution of the equation is eventually periodic with a prescribed period. 3. Every solution of the equation converges to a periodic solution with the same period. This monograph presents their findings along with some thought-provoking questions and many open problems and conjectures worthy of investigation. The authors also propose investigation of the global character of solutions of these equations for other values of their parameters and working toward a more complete picture of the global behavior of their solutions. With the results and discussions it presents, Periodicities in Nonlinear Difference Equations places a few more stones in the foundation of the basic theory of nonlinear difference equations. Researchers and graduate students working in difference equations and discrete dynamical systems will find much to intrigue them and inspire further work in this area.

About the Author

E.A. Grove, G. Ladas