الصفحة 1
الصفحة 1
Mechanics : From Newton's Laws to Deterministic Chaos
This updated and revised fourth edition covers all topics in mechanics from elementary Newtonian mechanics, canonical and rigid body mechanics to relativistic mechanics and nonlinear dynamics. In particular, symmetries and invariance principles, geometrical structures and continuum mechanics play an important role. This book will enable the reader to develop general principles from which equations of motions may be derived, to understand the importance of symmetries as a basis for quantum mechanics and to get practice in using theoretical tools and concepts that are essential for all branches of physics. The book contains numerous problems with complete solutions, and some practical examples.This will be appreciated in particular by students using the text to accompnay lectures on mechanics. The book ends with some historical remarks on important pioneers in mechanics.
High-dimensional chaotic and attractor systems : A comprehensive introduction
If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book.
Economics: Complex Windows
This volume contains papers that provide an analysis of topics in the following areas: Agent Based Models, Non-linear Time Series Analysis, Financial Market Dynamics, Econo-physics, Deterministic Chaos, Macroeconomic Dynamics. Economics: Complex Windows, does not present contributions to the sterile debate as to the merits of the different grand, or potentially grand paradigms of economics. Rather it offers a balanced collection of methodological advances which can be applied to concrete economic problems. Starting with a presentation of the "complexity approach" to economics, it goes on to provide a collection of applications to areas such as the analysis of market imperfections, risk assessment, non-linear dynamics, forecasting and highly irregular fluctuations. The tools used help to provide a clearer understanding and a more accurate analysis of these areas of economics. They also highlight the gulf which exists between current economic theory and real economic practice. The basic idea is to encourage economic researchers to embrace a more open and pragmatic approach to economics rather than to reluctantly move in this direction as if it were somehow a betrayal of established dogma. We hope, in this way, to open up avenues which will lead to progress beyond the "holy trinity", (rationality, equilibrium and greed) of modern economics.
Chaos and fractals : New frontiers of science
Covers the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors.
Chaos : A Program Collection for the PC
This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details. For the third edition of Chaos: A Program Collection for the PC, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two-dimensional problems, which is introduced in Chapter 13. Each chapter follows the structure: theoretical background; numerical techniques; interaction with the program; computer experiments; real experiments and empirical evidence; reference.
