Statistical Physics, Dynamical Systems and Complexity.
Dinamicheskie sistemy 5
Bifurcation theory and catastrophe theory
Dynamical systems 5. Bifurcation theory and catastrophe theory / V. I. Arnol'd (ed.). [Transl. N. Kazarinoff]
Dynamical systems. 5, Bifurcation theory and catastrophe theory
Dynamical systems
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.
Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, Vol. 5, Dinamicheskie Sistemy 5
Dynamical systems 3. Mathematical Aspects of Classical and Celestial Mechanics
Dynamical systems. 3, Mathematical aspects of classical and celestial mechanics
Dynamical systems. 5., Bifurcation theory and catastrophe theory
Mathematical aspects of classical and celestial mechanics
Dynamical Systems V Bifurcation Theory and Catastrophe Theory
Itogi nauki i tehniki. Sovremennye problemy matematiki. Fundamentalnye napravleniâ. Vol.5, Dinamičeskie sistemy 5
Dynamical systems. 5, Bifurcation theory and catastrophe theory / V. I. Arnol'd (ed.)
Dynamical systems 3. Mathematical aspects of classical and celestial mechanics / V. I. Arnold (ed.). [Authors V. I. Arnold ... Transl. A. Iacob]
Electronic books
Dynamical systems 5
This work describes the fundamental principles, problems, and methods of classical mechanics. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics, rather than its physical foundations or applications. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Chapter 2 presents the n-body problem as a generalization of the 2-body problem. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Chapter 4 contains a brief survey of various approaches to the problem of the integrability of the equations of motion. Chapter 5 is devoted to one of the most fruitful branches of mechanics - perturbation theory. Chapter 6 is related to chapters 4 and 5, and studies the theoretical possibility of integrating the equations of motion. Elements of the theory of oscillations are given in chapter 7. The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects. The "Encyclopaedia of Mathematical Sciences" addresses all mathematicians, physicists and enigneers.
Dinamicheskie sistemy 3
Dynamical systems five
Dynamical systems. / V.I. Arnold (ed.)
Dynamical systems, 3: Mathematical aspects of classical and celestial mechanics
Dynamical systems / III, Mathematical aspects of classical and celestial mechanics / V.I. Arnold (ed.)
Dynamical systems III : mathematical aspects of classical and celestial mechanics
Dynamical systems. III, Mathematical aspects of classical and celestial mechanics
Dynamical systems 3. : mathematical aspects of classical and celestial mechanics
Dynamical systems. V, Bifurcation theory and catastrophe theory
Dynamical systems 3
Dynamical systems V ; bifurcation theory and catastrophe theory
Dinamicheskie sistemy
Dynamical systems. 3, Mathematical aspects of classical and celestial mechanics / V. I. Arnold (ed.)
Dynamical systems. Vol. 5, Bifurcation theory and catastrophe theory
Dynamical systems V : bifurcation theory and catastrophe theory