Complex Dynamics
Advanced System Dynamics in Complex Variables
Buch in deiner Nähe kaufen
Beschreibung
Complex Dynamics: Advanced System Dynamics in Complex Variables is a graduate-level monographic textbook. It has seven Chapters. The introductory Chapter 1 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. Chapter 2 develops low-dimensional dynamics in the complex plane, theoretical and computational, continuous- and discrete-time. Chapter 3 presents a modern introduction to quantum dynamics, mainly following Dirac's notation. Chapter 4 develops geometrical machinery of complex manifolds, essential for the further text. Chapter 5 develops high-dimensional complex continuous dynamics, which takes place on complex manifolds. Chapter 6 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, Chapter 7, 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.
Unique dynamics in complex variables Predictive power of complex-valued geometry and topology in real life Unified to complex systems of various natures Complex path integrals in physics, biophysics, psychophysics, sociophysics and econophysics
Autor*in
Vladimir G. Ivancevic
Themen in »Complex Dynamics«
Complex path integrals Geometrical dynamics Nonlinear systems dynamics in complex variables Unified complex-geometrical methods
Stimmen zu »Complex Dynamics«
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)
()