Laura Gardini - Böcker

Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed byMira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were

This compelling book presents remarkable contributions from esteemed speakers who participated in the 28th International Conference on Difference Equations and Applications, ICDEA 2023, hosted at Phitsanulok, Thailand, in collaboration with the International Society of Difference Equations (ISDE) from July 17 to 21, 2023.

This compelling book presents remarkable contributions from esteemed speakers who participated in the 28th International Conference on Difference Equations and Applications, ICDEA 2023, hosted at Phitsanulok, Thailand, in collaboration with the International Society of Difference Equations (ISDE) from July 17 to 21, 2023. Embark on an enriching journey through the realms of difference equations and discrete dynamical systems, with practical applications spanning economics, engineering, biology, and related sciences. Immerse yourself in cutting-edge research as you explore new and significant breakthroughs within the fields of difference equations and discrete dynamical systems. This comprehensive compilation spans diverse scientific disciplines, demonstrating the profound impact of these theories and methodologies in practical and tangible settings.From economic modeling to engineering optimization, from biological systems to interdisciplinary applications, this book exemplifies the versatility and relevance of difference equations and discrete dynamical systems. Designed to resonate with a wide audience, including Ph.D. students, researchers, educators, and practitioners, it goes beyond mere dissemination of recent results. It actively fosters the advancement of knowledge, serving as a catalyst for further explorations and innovations across the spectrum of sciences.

This proceedings volume gathers selected and invited contributions presented at the 29th International Conference on Difference Equations and Applications (ICDEA), held in Paris, France, from June 24 to 28, 2024. Papers in this volume cover topics in the theory and applications of difference equations and discrete dynamical systems in fields as diverse as mathematical economics, mathematical biology, and others, offering a glimpse of the state of the art in these fields.Organized by the International Society of Difference Equations (ISDE) since 1994, the ICDEA has become an invaluable opportunity for experts and students worldwide to share their findings and foster avenues of cooperation. Volumes from previous iterations of ICDEA are also available from Springer.

Over the last two decades there has been a great deal of research into nonlinear dynamic models in economics, finance and the social sciences. This book contains twenty papers that range over very recent applications in these areas. Topics covered include structural change and economic growth, disequilibrium dynamics and economic policy as well as models with boundedly rational agents. The book illustrates some of the most recent research tools in this area and will be of interest to economists working in economic dynamics and to mathematicians interested in seeing ideas from nonlinear dynamics and complexity theory applied to the economic sciences.

Over the last two decades there has been a great deal of research into nonlinear dynamic models in economics, finance and the social sciences. This book contains twenty papers that range over very recent applications in these areas. Topics covered include structural change and economic growth, disequilibrium dynamics and economic policy as well as models with boundedly rational agents. The book illustrates some of the most recent research tools in this area and will be of interest to economists working in economic dynamics and to mathematicians interested in seeing ideas from nonlinear dynamics and complexity theory applied to the economic sciences.

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.