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Dynamical Systems IX - Dynamical Systems with Hyperbolic Behaviour (Hardcover, 1995 ed.): D.V. Anosov Dynamical Systems IX - Dynamical Systems with Hyperbolic Behaviour (Hardcover, 1995 ed.)
D.V. Anosov; Contributions by D.V. Anosov; Translated by G.G. Gould; Contributions by S.K. Aranson, V.Z Grines, …
R2,929 Discovery Miles 29 290 Ships in 10 - 15 working days

This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details)."

Dynamical Systems IX - Dynamical Systems with Hyperbolic Behaviour (Paperback, Softcover reprint of hardcover 1st ed. 1995):... Dynamical Systems IX - Dynamical Systems with Hyperbolic Behaviour (Paperback, Softcover reprint of hardcover 1st ed. 1995)
D.V. Anosov; Contributions by D.V. Anosov; Translated by G.G. Gould; Contributions by S.K. Aranson, V.Z Grines, …
R2,789 Discovery Miles 27 890 Ships in 10 - 15 working days

This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details)."

Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Paperback, Softcover reprint of the... Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Paperback, Softcover reprint of the original 1st ed. 1988)
D.V. Anosov; D.V. Anosov; Translated by E.R. Dawson, D. O'Shea; Edited by V. I. Arnol'd; …
R2,853 Discovery Miles 28 530 Ships in 10 - 15 working days

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." "Journal de Physique"

Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Hardcover, 1st ed 1988. 2nd printing 1994):... Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Hardcover, 1st ed 1988. 2nd printing 1994)
D.V. Anosov; D.V. Anosov; Translated by E.R. Dawson, D. O'Shea; Edited by V. I. Arnol'd; …
R2,806 Discovery Miles 28 060 Ships in 10 - 15 working days

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." "Journal de Physique"

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