Dynamical Systems has 8 ratings and 1 review. Woflmao said: This has got the be the messiest book I have ever read, math or non-math. The number of typos. Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the. Shlomo Sternberg’s book Dynamical Systems is that excellent introduction which many of us sought when we were first-year graduate students, who became.
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Why is one interested in fixed point theorems?
Shlomo Sternberg, Dynamical systems
ehlomo He has written several papers with Yuval Ne’eman on the role of supersymmetry in elementary particle physics in which they explore from this perspective the Higgs mechanismthe method of spontaneous symmetry breaking and a unified approach to the theory of quarks and leptons. To ask other readers questions about Dynamical Systemsplease sign up.
Dtgomm rated it really liked it Feb 07, Many of Sternberg’s other papers have been concerned with Lie group actions on symplectic manifolds. The difficulty ranges from elementary calculus to serious real analysis, so it is manageable. Elsa Rubio rated it it was amazing Nov 25, Stefan added it Apr 12, Dover Books on Mathematics. Shlomo Zvi Sternberg bornis an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory.
Want to Read Currently Reading Read. Elizabeth Aedyn River marked it as to-read Apr 20, This figures in GQS as an analytical detail in their classification proof but is nowadays the most cited result of the paper. Tom Fitz added it Feb 17, Trivia About Dynamical Systems. Want to Read saving…. Johan Lord marked it as to-read Dec 06, Lists with This Book. Group theory and physics by S. Retrieved from ” https: This became the basis for his first well-known published result known as the “Sternberg linearization theorem” which asserts that a smooth map near a hyperbolic fixed point can be made linear by a smooth change of coordinates provided that certain non-resonance conditions are satisfied.
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“Dynamical Systems” by Shlomo Sternberg
At some points whole paragraphs were missing, at other, some paragraphs apparently were copied-and-pasted twice, and then some LaTeX commands pop up in the middle of a sentence. International Press of Boston.
Also, in a sequel to this paper written jointly with Victor Guillemin and Daniel Quillenhe extended this classification to a larger class of pseudogroups: To see what your friends thought of this book, please sign up. Refresh and try again. The first eight chapters which correspond to lecture notes on Sternberg’s website mainly focus on fixed point theorems for contracting maps, and applications of these theorems.
Ray added it Aug 31, This chapter, together with chapter 8, is already the most difficult one, so that the rest of the book is not too hard to follow. Sheldon marked it as to-read Feb 09, Books by Shlomo Sternberg. One important by-product of the GQS paper was the ” integrability of characteristics” theorem for over-determined systems of partial differential equations.
There are no discussion topics on this book yet. Sternberg has, in addition, played a role in recent developments in theoretical physics: The book is very efficient in the sense that it progresses to the main results without much ado. Return to Book Page.
Daniel Mahler marked it as to-read Dec 02, What I particularly liked about the book is that it uses and encourages an experimental use of mathematics, that is, doing numerical experiments, plotting graphs of functions to find fixed points or periodic points and then, after the experiment, supply a proof to confirm the observations. In the first of these papers Bertram Kostant and Sternberg show how reduction techniques enable one to give a rigorous mathematical treatment of what is known in the physics literature as the BRS quantization procedure; in the second, dynamicao authors show how one can simplify the analysis of complicated dynamical systemw like the Calogero system by describing these systems as symplectic reductions of much simpler systems, and the paper with Victor Guillemin contain the first rigorous formulation and proof of a hitherto vague assertion about group actions on symplectic manifolds ; the assertion that “quantization commutes with reduction”.
From chapter 9 on, the chapters seem hastily slammed together, there is much less cohesion than in the first part of the book, and the motivation for what is done is much less clear. Peter marked it as to-read Dec 28, An account of these results and of their implications for the theory of dynamical systems can be found in Bruhat ‘s exposition “Travaux de Sternberg”, Seminaire Bourbaki, Volume 8. Sternberg’s contributions to symplectic geometry and Lie theory have also included a number of basic textbooks on these subjects, among them the three graduate level texts with Victor Guillemin: Peder added it Nov 06, This page was last edited on 16 Mayat Please help to improve this article by introducing more precise citations.
He also published the more recent “Curvature in mathematics and physics”. Dec 17, Woflmao rated it liked it Shelves: Alexander marked it as to-read Mar 03, Will aternberg it as to-read Jan 19, Shlomo Zvi Sternberg is a leading mathematician, known for his work in geometry, particularly symplectic geometry and the differential geometry of G-structures.