Book Review

Dynamics of One—Dimensional Maps by A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak and Y. V. Fedorenko, Publisher: Kluwer Academic Publishers, Format: Hardcover, Publication Date: April 1997, 260 Pages. ISBN: 07923-4532-0, Price: $196=00. This is a nice and interesting introductory book on the dynamics of 1—dimensional maps. As stated by the authors, the book has two main goals. The first is to introduce the readers to the fundamentals of the theory of 1—dimensional dynamical systems. The second is to provide to the readers a comprehensive view of the problems appearing in the theory of dynamical systems and to describe the methods used to solve these problems in the case of 1—dimensional maps. The first chapter of this book is an elementary introduction to the theory of 1—dimensional maps. It contains an exposition of basic concepts of the theory of dynamical systems and a list of examples illustrating various situations encountered in the study of 1—dimensional maps. The second chapter deals with symbolic dynamics. It contains in particular a presentation of the kneading theory. The third chapter is on the Sharkovsky theorem, one of the most important early results in the theory of 1—dimensional maps. Chapter 4 contains, to a certain degree of details, a classification theory of 1—dimensional maps with zero entropy that mainly reflects the research interests of the authors. Chapter 5 is an introductory lecture to unimodal maps. Chapter 6 is on the aspect of 1—dimensional dynamics that is related to measure theory. Existence theorems on absolutely continuous invariant measures are discussed. Chapter 7 is on the problem of structure stability, and Chapter 8 is on fundamentals of 1—dimensional families of maps: bifurcation periodic doubling and universality.BOOK REVIEW This book touches a variety of topics, introduces basic concepts and presents many important early results that are fundamentally important to the study of 1—dimensional maps, Most of the materials the book covers have a distinctively topological flavor that occurs rather commonly in the study of dynamical systems up to the early 1980's. A substantial part of the text can be used directly in an introductory course on dynamical systems. On the other hand, readers should be reminded that there have been explosive new developments in the study of 1—dimensional maps since this book was written. One should definitely find books and survey articles that are more recent for an up—to—date view on this subject     

Book Review

Difference Equations Theory and Applications by Ronald E. Mickens, CRZ: Press LLC, Eioca Iiaron, Florida, Second Edition, Publicarion Date: 01 /Oi /9l, 4-43 pages. ISBN: 0442001363, Price: $69.95 US.     

Book Review

Linear difference equations with variable delay are considered. The most important result of this paper is a new oscillation criterion, which should be looked upon as the discrete analogue of a well-known oscillation criterion for first order linear delay differential equations. This criterion constitutes a substantial improvement of an oscillation result due to the first author (Funkcial. Ekvac. 34 (1991), pp. 157–172). The results obtained extend the ones by the authors and Stavroulakis (J. Differ. Equ. Appl. 10 (2004), pp. 419–435) concerning the special case of linear difference equations with constant delay.     

Book Review

Book reviewed in this article: Hurlbut, Cornelius S. Jr., (Ed.), The Planet We Live On: An Illustrated Encyclopedia of the Earth Sciences. New York: Harry N. Abrams 100 Geometric Games, by Pierre Berloquin.     

Book Review

Book Review

Book Review     

Book Review

A method of estimation of the coefficients of a linear regression model is described as invariant if the basic regression results obtained by the method are unaltered by a location/scale transformation of the data matrix. A necessary and sufficient condition for a method to be invariant is presented. Finally specific methods of estimation are examined for invariance.     

Book Review

Book reviewed in this article: Noll, Edward M., Wind/Solar Energy for Radiocommunkations and Low-Power Electronic/Electric Applications. Lloyd, Francis Ernest, The Carnivorous Plants.     

Book Review

Book reviewed in this article: Moving Right Along—A Book of Science Experiments and Puzzlers About Motion, by Robert Gardner and David Webster