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Synopsis
This third edition has been substantially revised and updated, with fresh chapters and augmented bibliographical references. It remains a very detailed and profound mathematical treatment of the long-term behavior of randomly perturbed dynamical systems.
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Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften, 260)
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Random Perturbations of Dynamical Systems
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Random Perturbations of Dynamical Systems (Hardcover)
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Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2012
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Hardcover. Etat : new. Hardcover. Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been rediscovered in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783642258466
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Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften, 260)
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Random perturbations of dynamical systems. Die Grundlehren der mathematischen Wissenschaften; 260.
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Berlin, Springer, 2012
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Hardcover. 3. ed. XXVIII, 458 S. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00707 9783642258466 Sprache: Englisch Gewicht in Gramm: 1050. N° de réf. du vendeur 2483233
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Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften, 260)
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Random Perturbations of Dynamical Systems
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Springer, 2012
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ISBN 13 : 9783642258466
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Random Perturbations of Dynamical Systems
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Springer Berlin Heidelberg Jun 2012, 2012
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been 'rediscovered' in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important. 488 pp. Englisch. N° de réf. du vendeur 9783642258466
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Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften, 260)
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