Author : W Forg-rob
Publisher : World Scientific
Page : 298 pages
File Size : 29,4 MB
Release : 1996-07-03
Category :
ISBN : 9814547891
Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms 'orbit' and 'chaos' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.
Author :
Publisher :
Page : 256 pages
File Size : 49,43 MB
Release : 2006
Category : Iterative methods (Mathematics)
ISBN :
Author : Janos Aczel
Publisher : Birkhäuser
Page : 218 pages
File Size : 22,61 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034890966
The journal aequationes mathematicae publishes papers in pure and applied mathematics and, in particular, articles on functional equations, combinatorics and dynamical systems. Its 50th volume appears in 1995. To mark this occasion, we are publishing in book form a repre sentative collection of outstanding survey papers assembled for our anniversary issue of aequationes mathematicae. The articles by Quackenbush, Targonski and Moszner discuss composition of functions from different points of view: universal algebra, dynamical systems (iteration) and functional equa tions. The Ono-Robbins-Wahl and the Vince papers, on number theory and tiles, respectively, are thematically linked by lattices. Combinatorics, in turn, links the Vince paper with that of Tutte, whose subject is chromatic sums, its tools differential and functional equations. The Paganoni-Ratz and the Forti papers deal with conditional functional equations and with the related topic of stability. Applications to the social and behavioral sciences, in particular to aggregation (and some theory) are presented in the paper by J. Aczel. The aim of the collection is to survey selected fields of current interest. We trust that it will be useful and informative for researchers, teachers, graduate and advanced undergraduate stu dents of mathematics, and for those interested in applications in related fields. lanDs Aczel Aequationes Mathematicae 50 (1995) 1 0001-9054/95/020001-01 $1.50 + 0.20/0 University of Waterloo © 1995 Birkhiiuser Verlag, Basel Editorial Volume 50 of Aequationes Mathematicae This is the fiftieth volume of aequationes mathematicae. Not only our modesty but also lack of space keeps us from self-congratulation.
Author : Sylvie Ruette
Publisher : American Mathematical Soc.
Page : 231 pages
File Size : 14,49 MB
Release : 2017-03-02
Category : Mathematics
ISBN : 147042956X
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the “most interesting” part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.
Author : Themistocles M. Rassias
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 15,89 MB
Release : 2011-09-18
Category : Mathematics
ISBN : 1461400554
The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.
Author : C. Mira
Publisher : World Scientific
Page : 638 pages
File Size : 28,88 MB
Release : 1996
Category : Mathematics
ISBN : 9789810216474
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.
Author : Wai-kai Chen
Publisher : World Scientific
Page : 871 pages
File Size : 50,59 MB
Release : 1999-07-03
Category : Science
ISBN : 9814496626
Authoritative and visionary, this festschrift features 12 highly readable expositions of virtually all currently active aspects of nonlinear science. It has been painstakingly researched and written by leading scientists and eminent expositors, including L Shilnikov, R Seydel, I Prigogine, W Porod, C Mira, M Lakshmanan, W Lauterborn, A Holden, H Haken, C Grebogi, E Doedel and L Chua; each chapter addresses a current and intensively researched area of nonlinear science and chaos, including nonlinear dynamics, mathematics, numerics and technology. Handsomely produced with high resolution color graphics for enhanced readability, this book has been carefully written at a high level of exposition and is somewhat self-contained.Each chapter includes a tutorial and background information, as well as a survey of each area's main results and state of the art. Of special interest to both beginners and seasoned researchers is the identification of future trends and challenging yet tractable problems that are likely to be solved before the end of the 21st century. The visionary and provocative nature of this book makes it a valuable and lasting reference.
Author : Philip A. Ebert
Publisher :
Page : 686 pages
File Size : 50,63 MB
Release : 2019
Category : Mathematics
ISBN : 0198712081
This is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Laws of Arithmetic, and demonstrate the technical and philosophical richness of this great work.
Author : Jacques Bélair
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 17,51 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 9401579318
This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.
Author : José Ferreirós Domínguez
Publisher : Oxford University Press, USA
Page : 455 pages
File Size : 16,89 MB
Release : 2006-04-27
Category : Mathematics
ISBN : 0198567936
Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.
