Ebook Download The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma
Based upon the The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma information that we offer, you could not be so baffled to be here as well as to be member. Get now the soft documents of this book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma and also wait to be your own. You conserving can lead you to stimulate the simplicity of you in reading this book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma Even this is types of soft documents. You could really make better opportunity to get this The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma as the recommended book to check out.
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma
Ebook Download The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma
Why ought to get ready for some days to obtain or obtain guide The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma that you purchase? Why ought to you take it if you can obtain The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma the faster one? You can find the exact same book that you buy right here. This is it the book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma that you can get directly after acquiring. This The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma is popular book on the planet, of course lots of people will certainly attempt to own it. Why don't you end up being the initial? Still perplexed with the way?
When getting this book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma as referral to review, you could get not just inspiration but also new understanding and also driving lessons. It has even more compared to common advantages to take. What type of book that you read it will serve for you? So, why ought to get this e-book entitled The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma in this article? As in web link download, you can get guide The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma by on-line.
When getting the book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma by online, you could read them any place you are. Yeah, also you are in the train, bus, waiting list, or other places, on the internet book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma can be your good friend. Whenever is a great time to review. It will improve your knowledge, fun, entertaining, lesson, and encounter without spending more money. This is why online e-book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma becomes most really wanted.
Be the first that are reading this The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma Based upon some factors, reading this e-book will provide even more perks. Also you should review it tip by step, web page by web page, you could complete it whenever and anywhere you have time. Once again, this online e-book The KAM Story: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-Arnold-Moser Theory, By H.S. Duma will give you easy of reviewing time as well as activity. It likewise offers the experience that is affordable to get to and obtain considerably for far better life.
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.
The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a "breakthrough"). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).
Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Readership: Undergraduates, graduates, and researchers broadly interested in Hamiltonian perturbation theory, statistical mechanics, ergodic theory, Nekhoroshev theory, Arnold diffusion, nonlinear dynamics, dynamical systems, chaos theory, classical mechanics, and the history of these subjects.
- Sales Rank: #1887063 in Books
- Published on: 2014-05-04
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .88" w x 5.98" l, 1.49 pounds
- Binding: Hardcover
- 380 pages
Review
"The mathematics is described in a very engaging style, with the focus being on 'ideas and motivation'. The narrative is developed through a historical description of the 'people side' of the struggles to achieve a deeper understanding of fundamental questions in dynamics. The book gives a very illuminating and inspiring account of how mathematical results are developed over time and across cultures in the broad context of the development of one of the great rigorous mathematical results of the last century — the KAM theorem." -- Prof Stephen Wiggins, University of Bristol
From the Inside Flap
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.
The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a "breakthrough"). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).
Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Most helpful customer reviews
7 of 7 people found the following review helpful.
The more mathematical sections are handled in a clear and cool, professional style
By William Kirk
The author of The KAM Story, A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory , H. Scott Dumas, has largely delivered on his title. This book is for those who have perhaps heard about “KAM theory”, or maybe even met the phrase “the celebrated KAM theorem” (a pet peeve of the author) in their studies or researches, and wondered what it was all about. The author himself would probably rather refer to it as K-A-M + Nekhoroshev (+Aubry-Mather) theory, to name but the most prominent contributors. In any case, with a perky prose style he presents us with what is a genuinely unbiased, even bemused, tour of the history of ergodic dynamics and the n-body problem, leading up to the 20th century and the eponymous heroes of the story, including the transitional figures Ludwig Boltzmann and especially Henri Poincare’. The more mathematical sections are handled in a clear and cool, professional style. Those whose interest have been piqued and who work in related areas will not have much difficulty, in fact even undergraduates, and, dare I say, talented high school students can slog through most of this material with help of an extensive glossary section at the end. One may otherwise have to refresh oneself on some concepts from (algebraic) topology, as well as one’s familiarity with classical (Lagrangian-Hamiltonian) mechanics. But KAM theory is in fact the more rigorous, mathematical side of the picture - the empirical, computer-driven aspects of stochastic dynamics as studied in e.g. engineering, astronomy, or biophysics is only tangentially related to the techniques and problems Professor Dumas discusses here. The role of ‘rigor’ in mathematics itself being, for the author, one of his many subsidiary themes.
The author laments the relative obscurity in America of KAM theory, even for those invested in dynamics and trajectories (practitioners in molecular dynamics, perhaps, or the large group of aficionados in ‘stochastic resonance theory’). His book aims to rectify that situation.
For those less professionally interested in the topic, however, the historical and indeed philosophical narratives he provides are excellent and engaging. Dumas even provides a useful, not altogether whimsical, set of ‘cartoon’ illustrations of the “meaning of KAM”. For both kinds of readers, he has given a long if not exhaustive bibliography of texts and articles for further reading.
Dumas takes rather extraordinary care to be fair to all sides. This is not a shortcoming: you may be convinced at the end that KAM theory deserves to be called celebrated, or you may agree with the author himself, that it is a “widely known (though partially understood)”, yet nonetheless beautiful development of 20th century mathematics.
2 of 2 people found the following review helpful.
Interesting for chemistry students
By Majored in Chemistry
I was a chemistry student in graduate school. One of the lectures my teacher gave was about methyl iodide, CH3I, or written as I-CH3. The question was whether the chemical bond between I and C will be broken, given some energy initially to the methyl group CH3. Although the problem was supposed to be treated quantum mechanically, chemists had always thought of a molecule as a group of coupled oscillators with energy flowing back and forth. Therefore, Newtonian (classical) mechanics was helpful in gaining physical intuition and even qualitative results. In the case of methyl iodide, I-C is an oscillator and CH3 is another oscillator. The two oscillators are interacting (coupled) with each other. Chemists attempted to answer the question whether an initially excited oscillator will quickly spread the energy out to its coupled oscillators or will keep the energy to itself for a long time.
That was the first time when I heard about KAM: If there is no excitation, each oscillator will make small amplitude oscillations and barely talk to each other. If the excitation of one oscillator is not strong and the frequency ratios between the oscillators are not rational numbers then it is possible that the motion of the oscillators will not been affected to the point that a chemical bond will get broken. We did many numerical studies, i.e., running classical trajectories with different initial conditions and take Poincare surfaces of intersection and found both integrable and non-integrable motions at the same total energy given. KAM had already known this nearly half a century ago through rigorous mathematics rather than numerical studies, which was absolutely amazing.
A typical chemistry text description of the ergodic hypothesis was for gas molecules in a box separated equally in 2 compartments the state of all molecules on one side and half number of molecules on each side are equally probable, just as all other possible numbers distributions between the two compartments. That is to say, given a time long enough each of the above state will show up pretty much equal number of times. However, in reality the two scenarios of all the molecules in one compartment and exactly half of the molecules in each compartment are rarely seen. The most probable states are those with APPROXIMATELY one-half number of molecules in each compartment. This is the so called “most probable distribution” which is what an observer sees during a reasonable period of experimental time. The way that “most probable distribution” works is based on our lack of knowledge of the interactions between the gas molecules in the box and it is often stated that it is “both impossible and unnecessary” to know the detailed interactions between the molecules. KAM points out that it is completely possible that if dynamical reasons exist (say there exist other constants of the motion in addition to the total energy) all the molecules could spend a long time in one-half of the box.
There are so many things to learn from Dumas book that I bring it with me in my humble backpack everyday to read it everywhere, especially on my subway and bus commutes. The mathematically oriented minds will have much fun from reading the book and others will also have great fun by skipping a few chapters and still get an overview of KAM. I worked through Chapters 2, 3, and 4 and have learned a lot of mathematics and I am sure that chemists will benefit from them as well as other chapters of the entire book.
The book is hard bound and World Scientific did a great job printing and binding it. This is perhaps one of the most pretty books of WS published in 2014, in content and in cosmetics.
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma PDF
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma EPub
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma Doc
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma iBooks
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma rtf
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma Mobipocket
The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory, by H.S. Duma Kindle
Tidak ada komentar:
Posting Komentar