×
![]( "Buchcover ISBN 9789048176311")
Research
From the reviews:„The book under review presents, in a concise and simple manner, complex dynamical systems, both low- (such as flows in the complex-plane and Riemann sphere) and high-dimensional (flows in complex manifolds), within the continuous- and discrete-time pictures. a broad reflection of the current state of the science of complex dynamics. It is a valuable book to read for serious readers who are interested in the whole spectrum of problems related to complex-valued nonlinear dynamics and in how to directly apply them in the research.“ (Eugene Kryachko, Zentralblatt MATH, Vol. 1134 (12), 2008)
Complex Dynamics
Advanced System Dynamics in Complex Variables
von Vladimir G. Ivancevic und Tijana T. IvancevicComplex Dynamics: Advanced System Dynamics in Complex Variables is a graduate-level monographic textbook. It is designed as a comprehensive introduction into methods and techniques of modern complex-valued nonlinear dynamics with its various physical and non-physical applications. This book is a complex-valued continuation of our previous two monographs, Geometrical Dynamics of Complex Systems and High-Dimensional Chaotic and Attractor Systems, Volumes 31 and 32 in the Springer book series Intelligent Systems, Control and Automation: Science and Engineering, where we had developed the most powerful mathematical machinery to deal with high-dimensional nonlinear, attractor and chaotic real-valued dynamics. The present monograph is devoted to understanding, prediction and control of both low- and high-dimensional, as well as both continuous- and discrete-time, nonlinear systems dynamics in complex variables. Its objective is to provide a serious reader with a serious scientific tool that will enable him/her to actually perform a competitive research in modern complex-valued nonlinear dynamics.
This book has seven Chapters. The first, introductory Chapter explains 'in plain English' the objective of the book and provides the preliminaries in complex numbers and variables; it also gives a soft introduction to quantum dynamics. The second Chapter develops low-dimensional dynamics in the complex plane, theoretical and computational, continuous- and discrete-time. The third Chapter presents a modern introduction to quantum dynamics, mainly following Dirac's notation. The fourth Chapter develops geometrical machinery of complex manifolds, essential for the further text. The fifth Chapter develops high-dimensional complex continuous dynamics, which takes place on complex manifolds. The sixth Chapter develops the formalism of complex path integrals, which extends the continuous dynamics to the general high-dimensional dynamics, which can be both discrete and stochastic. In the last, seventh Chapter, all previously developed methods are employed to present the 'Holy Grail' of modern physical and cosmological science, the search for the 'theory of everything' and the 'true' cosmological dynamics.
This book has seven Chapters. The first, introductory Chapter explains 'in plain English' the objective of the book and provides the preliminaries in complex numbers and variables; it also gives a soft introduction to quantum dynamics. The second Chapter develops low-dimensional dynamics in the complex plane, theoretical and computational, continuous- and discrete-time. The third Chapter presents a modern introduction to quantum dynamics, mainly following Dirac's notation. The fourth Chapter develops geometrical machinery of complex manifolds, essential for the further text. The fifth Chapter develops high-dimensional complex continuous dynamics, which takes place on complex manifolds. The sixth Chapter develops the formalism of complex path integrals, which extends the continuous dynamics to the general high-dimensional dynamics, which can be both discrete and stochastic. In the last, seventh Chapter, all previously developed methods are employed to present the 'Holy Grail' of modern physical and cosmological science, the search for the 'theory of everything' and the 'true' cosmological dynamics.
