Sharkovsky's Theorem, Li and Yorke's "period 3 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.
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 dynamic systems will find much to intrigue them and inspire further work in this area.
Over the last ten years, Grove and Ladas (both: mathematics, U. of Rhode Island) have devoted their efforts to discovering periodicities in higher-order nonlinear difference equations. Aimed at researchers and graduate students, this monograph presents their findings while identifying some open problems and conjectures that merit further investigation. The authors also propose an examination of the global character of solutions of these equations for other values of their parameters, and suggest working toward a more complete picture of the global behavior of their solutions. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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.
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