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Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2009-10-22
Total Pages: 500
ISBN-13: 3642017428
DOWNLOAD EBOOKVladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2013-12-11
Total Pages: 458
ISBN-13: 3642310311
DOWNLOAD EBOOKVladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2004-06-24
Total Pages: 664
ISBN-13: 9783540206149
DOWNLOAD EBOOKVladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 530
ISBN-13: 1475720637
DOWNLOAD EBOOKThis book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author: Vadim Kaloshin
Publisher: Princeton University Press
Published: 2020-11-03
Total Pages: 218
ISBN-13: 0691202524
DOWNLOAD EBOOKThe first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.
Author: Vladimir Igorevich Arnold
Publisher: Springer Science & Business Media
Published: 1993
Total Pages: 264
ISBN-13: 9783540505839
DOWNLOAD EBOOK'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.
Author: Vladimir I. Arnold
Publisher: Springer
Published: 2010-02-12
Total Pages: 0
ISBN-13: 9783642066863
DOWNLOAD EBOOKThis is a charming collection of essays on life and science, by one of the leading mathematicians of our day. Vladimir Igorevich Arnold is renowned for his achievements in mathematics, and nearly as famous for his informal teaching style, and for the clarity and accessibility of his writing. The chapter headings convey Arnold’s humor and restless imagination. A few examples: My first recollections; The combinatorics of Plutarch; The topology of surfaces according to Alexander of Macedon; Catching a pike in Cambridge. Yesterday and Long Ago offers a rare opportunity to appreciate the life and work of one of the world’s outstanding living mathematicians.
Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
Published: 2014-09-04
Total Pages: 184
ISBN-13: 1470418894
DOWNLOAD EBOOK"This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science."--
Author: Boris A. Khesin
Publisher: American Mathematical Society
Published: 2014-09-10
Total Pages: 221
ISBN-13: 1470416999
DOWNLOAD EBOOKVladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.
Author: Sze-bi Hsu
Publisher: World Scientific Publishing Company
Published: 2013-06-07
Total Pages: 312
ISBN-13: 9814452920
DOWNLOAD EBOOKDuring the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
