Download PDF by H.S. Dumas: The KAM Story: A Friendly Introduction to the Content,

Download PDF by H.S. Dumas: The KAM Story: A Friendly Introduction to the Content,

By H.S. Dumas

This can be a semi-popular arithmetic e-book aimed toward a wide readership of mathematically literate scientists, specifically mathematicians and physicists who're no longer specialists in classical mechanics or KAM conception, and scientific-minded readers. components of the ebook also needs to attract much less mathematically knowledgeable readers with an curiosity within the historical past or philosophy of technology.

The scope of the booklet is huge: it not just describes KAM thought in a few element, but additionally offers its ancient context (thus exhibiting why it used to be a "breakthrough"). additionally mentioned are purposes of KAM conception (especially to celestial mechanics and statistical mechanics) and the elements of arithmetic and physics during which KAM thought is living (dynamical platforms, classical mechanics, and Hamiltonian perturbation theory).

even though a few resources on KAM thought at the moment are on hand for specialists, this e-book makes an attempt to fill a long-standing hole at a extra descriptive point. It sticks out very in actual fact from present courses on KAM idea since it leads the reader via an obtainable account of the idea and areas it in its right context in arithmetic, physics, and the historical past of science.

Readership: Undergraduates, graduates, and researchers greatly drawn to Hamiltonian perturbation idea, statistical mechanics, ergodic concept, Nekhoroshev concept, Arnold diffusion, nonlinear dynamics, dynamical structures, chaos concept, classical mechanics, and the background of those matters.

Show description

Read Online or Download The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory PDF

Best mathematical physics books

Uncertainty and Surprise in Complex Systems: Questions on - download pdf or read online

Complexity technology has been a resource of recent perception in actual and social structures and has tested that unpredictability and shock are primary features of the realm round us. This ebook is the result of a dialogue assembly of major students and important thinkers with services in advanced platforms sciences and leaders from numerous agencies, backed via the Prigogine heart on the college of Texas at Austin and the Plexus Institute, to discover suggestions for figuring out uncertainty and shock.

Download e-book for iPad: Mathematics of Physics and Engineering: Selected Topics by Edward K Blum, Sergey V Lototsky

Aimed toward scientists and engineers, this booklet is an exhilarating highbrow trip during the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac. whereas comparable books current the necessary arithmetic in a piecemeal demeanour with tangential references to the appropriate physics and engineering, this textbook serves the interdisciplinary wishes of engineers, scientists and utilized mathematicians through unifying the maths and physics right into a unmarried systematic physique of data yet conserving the rigorous logical improvement of the maths.

Download e-book for kindle: A History of the Study of Mathematics at Cambridge by Walter William Rouse Ball

For hundreds of years, Cambridge collage has attracted many of the world's maximum mathematicians. This 1889 booklet provides a compelling account of the way arithmetic built at Cambridge from the center a long time to the past due 19th century, from the point of view of a number one student dependent at Trinity collage who used to be heavily all for instructing the topic.

Additional resources for The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory

Sample text

Although Poincaré’s work was amply recognized in his lifetime, many parts remained enigmatic long afterward. As more nuggets were dug from his Nachlass and it was realized how far ahead of his time he was, there emerged a tendency to read his works line-by-line, like sacred texts. These ‘exegetical Poincaré studies’ did (and do) occasionally lead to new insights into the master’s meaning, but on the whole it’s amusing to imagine what Poincaré might make of the close scrutiny given to writings that he himself took less seriously38 It’s also interesting to ponder the severe and mostly no-fun reaction to Poincaré’s intuitionist style in the decades after his death.

5 A proxy r ω2 /ω1 for the frequency map (I1, I2) (ω1,ω2) showing (a) a nondegenerate case, (b) a degenerate case. In case (b), the interval [r1,r2] is collapsed to the point p under the proxy map. Finally here’s a key fact we’ll return to below: For a nondegenerate system with n = 2, as we move out radially in r (Fig. 2), the resonant tori are distributed among the nonresonant tori in the same way that the rational numbers are distributed among the irrationals. 31 This will be important, because one of the main messages of KAM theory is that, when a nondegenerate integrable system is perturbed, its resonant tori (along with some others ‘close to resonant’) break up chaotically, while a large subset of its nonresonant tori survive and are only slightly distorted.

This has been told many times and at various levels of detail (it is described in Chapter 7 of [Pete93] by I. Peterson, in Chapter 1 of [DiH96] by F. Di-acu and P. Holmes, and it is the essential core of the book [Barro97] by J. Barrow-Green), so I give here only the barest outline, in a present-tense, stage-direction style. The stage opens in Berlin in the early 1880s where we find Karl Weierstrass (1815– 1897) keenly interested in the n body problem. Weierstrass is probably the world’s leading figure in mathematics, rising from humble beginnings as a Gymnasium teacher in Münster (1841) to full professor at the University of Berlin (1856).

Download PDF sample

Rated 4.58 of 5 – based on 28 votes
Comments are closed.