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by V. I. Arnol'D,G. S. Wassermann
Download Catastrophe Theory fb2
Mathematics
  • Author:
    V. I. Arnol'D,G. S. Wassermann
  • ISBN:
    0387548114
  • ISBN13:
    978-0387548111
  • Genre:
  • Publisher:
    Springer Verlag; Revised, Expanded, Subsequent edition (September 1, 1992)
  • Pages:
    150 pages
  • Subcategory:
    Mathematics
  • Language:
  • FB2 format
    1573 kb
  • ePUB format
    1341 kb
  • DJVU format
    1688 kb
  • Rating:
    4.5
  • Votes:
    915
  • Formats:
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If only one were as enthusiastic as Arnol'd about singularity classification theorems then this would be very interesting indeed. 13 people found this helpful.

If only one were as enthusiastic as Arnol'd about singularity classification theorems then this would be very interesting indeed.

The book can be warmly recommended to everyone who is interested in singularity theory. Arnol'd instead prefers the mathematical meat and potatoes of catastrophe theory: the theory of singularities.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Catastrophe Theory. The book can be warmly recommended to everyone who is interested in singularity theory. If only one were as enthusiastic as Arnol'd about singularity classification theorems then this would be very interesting indeed.

Surviving Lamentations: Catastrophe, Lament, and Protest in the Afterlife of a Biblical Book. Heinz-Dieter Ebbinghaus, Jörg Flum. and questions of complexity theory and of database theory. literature of survival" (works written by survivors of catastrophe) as well as literary and philosophical reflections. Model theory or the theory of models, as it was.

Discover new books on Goodreads. See if your friends have read any of . Wassermann’s Followers. Catastrophe Theory by. Vladimir I. Arnold, . Wassermann (Translator).

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation

The author begins by describing the established results in the theory of singularities and bifurcation and continues with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control.

Springer-Verlag Berlin Heidelberg New York Tokyo. Vladimir Igorevich Arnold Department of Mathematics University of Moscow Moscow 117234 USSR.

Translated from the Russian by G. S. Wassermann Based on a Translation by R. K. Thomas. Springer-Verlag Berlin Heidelberg New York Tokyo.

Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvements to Quasicrystals. Teoriya bifurkacij (ru)(218s). Teorija katastrof (1990) (ru)(128s).

Arnol?d, V. I. (Vladimir Igorevich), 1937-2010. Download DOC book format. Arnold ; translated from the Russian by . Wassermann based on a translation by . book below: (C) 2016-2018 All rights are reserved by their owners.

Provides a concise, non-mathematical review of the less controversial results in catastrophe theory. The presentation is enhanced by numerous diagrams. DLC: Catastrophes (Mathematics)

Jerinovir
Catastrophe theory is introduced as a sort of merger of Whitney's theory of singularities of mappings and Poincaré's qualitative theory of dynamical systems. First Whitney. A surface is projected onto a plane. Somewhere the surface is folded, so that the inverse of the projection is multi-valued. Now, the plane may represent the possible values of the control parameters of a dynamic system, and the surface the possible states of the system. Moving continuously in the plane across the boundary between a single-valued and a multi-valued region may cause a jump on the surface to one of the other sheets--i.e. a small external change causes the system's state to change drastically: a "catastrophe". Poincaré's bifurcation theory of dynamical systems may now be perceived similarly on a metalevel where the systems themselves are points in a space--again an infinitesimal move in the system space may cause drastic changes of the system's equilibria. This type of geometric thinking may then be used in applications--but only sober ones, mind you: elasticity, optics, etc. Back in the old days Thom quite successfully pushed his catastrophe theory on gullible non-mathematicians. Arnol'd states his own view on those matters clearly and repeatedly throughout the book. From the preface: "Neither in 1965 nor later was I ever able to understand a word of Thom's own talks on catastrophes. He once described them to me as 'bla, bla, bla'". Arnol'd instead prefers the mathematical meat and potatoes of catastrophe theory: the theory of singularities. If only one were as enthusiastic as Arnol'd about singularity classification theorems then this would be very interesting indeed.
Walianirv
Catastrophe theory was the first mathematical "advance" to receive extensive coverage in the popular press since quantum mechanics. The interest and adulation afforded to chaos theory and nonlinear dynamical systems research barely immitated the enthusiasm and later scorn generated by Thom and his followers. In retrospect it is hard to see what all the excitement was about. Perhaps that's exactly why this book deserves serious attention.
While the doctoral trained mathematician may find more faults here than the rest of us, this book provides sufficient complexity for the professional, and at times is "gentle" enough for the nonmathematician. It will probably find its most useful audience among people with "semi-mathematical" trainings, scientists in life and behavioral or social sciences. For these people, who may just want to find out why Thom's initial theorems generated so much excitement and controversey, this book will be a readable delight.