Shlomo Zvi Sternberg born , is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. 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. Also proved were generalizations of the Birkhoff canonical form theorems for volume preserving mappings in n-dimensions and symplectic mappings, all in the smooth case. 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.
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This book is not yet featured on Listopia. Community Reviews. Showing Average rating 4. Rating details. More filters. Sort order. Start your review of Dynamical Systems. Dec 17, Woflmao rated it liked it Shelves: science , reviewed. This has got the be the messiest book I have ever read, math or non-math. The number of typos is unbelievable. 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.
Once one has set one's mind to bear with this mess, the book becomes ra This has got the be the messiest book I have ever read, math or non-math. Once one has set one's mind to bear with this mess, the book becomes rather enjoyable.
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. Why is one interested in fixed point theorems? A famous example is the Newton iteration, and this is in fact the topic of the first chapter of this book. 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.
The difficulty ranges from elementary calculus to serious real analysis, so it is manageable. 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.
The book is very efficient in the sense that it progresses to the main results without much ado. Most of the proofs are easy to follow, though the aforementioned typos and some random changes in notation can lead to confusion.
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. Based on the first eight chapters, I would have given the book four stars, but as a whole, I cannot bring myself to award more than three. Botkinbote rated it it was amazing Jul 04, Branko Nikovski rated it it was amazing Jun 17, Elsa Rubio rated it it was amazing Nov 25, GMK rated it really liked it May 30, Christian rated it it was amazing Jun 04, Dtgomm rated it really liked it Feb 07, Marco Spadini rated it really liked it Jun 25, Adam added it Sep 27, Peter marked it as to-read Dec 28, Sheldon marked it as to-read Feb 09, Ray added it Aug 31, Peder added it Nov 06, Nitin Rughoonauth added it Nov 16, Filip marked it as to-read Nov 27, Johan Lord marked it as to-read Dec 06, Alexander marked it as to-read Mar 03, Adam Centurione marked it as to-read Mar 16, Stefan added it Apr 12, Francesco marked it as to-read May 10, Jones marked it as to-read Aug 17, Daniel Mahler marked it as to-read Dec 02, Sutton marked it as to-read Jul 16, Lee Corbin added it Feb 25, Lawrence Lifshitz marked it as to-read Aug 08, Elizabeth Aedyn River marked it as to-read Apr 20, Dongliang Qin marked it as to-read Jul 20, Kevin Mansinthe marked it as to-read Dec 06, There are no discussion topics on this book yet.
Readers also enjoyed. About Shlomo Sternberg. Shlomo Sternberg. Shlomo Zvi Sternberg is a leading mathematician, known for his work in geometry, particularly symplectic geometry and the differential geometry of G-structures. Books by Shlomo Sternberg. Related Articles. For more than a decade, Neil deGrasse Tyson, the world-renowned astrophysicist and host of the popular radio and Emmy-nominated televi Read more Trivia About Dynamical Systems.
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Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains.