This is a semi-popular arithmetic booklet aimed toward a vast readership of mathematically literate scientists, particularly mathematicians and physicists who're now not specialists in classical mechanics or KAM conception, and scientific-minded readers. components of the publication also needs to attract much less mathematically knowledgeable readers with an curiosity within the background or philosophy of science.

The scope of the e-book is huge: it not just describes KAM thought in a few element, but in addition provides its ancient context (thus exhibiting why it used to be a “breakthrough”). additionally mentioned are functions of KAM idea (especially to celestial mechanics and statistical mechanics) and the components of arithmetic and physics during which KAM idea is living (dynamical platforms, classical mechanics, and Hamiltonian perturbation theory).

Although a few resources on KAM conception are actually to be had for specialists, this ebook makes an attempt to fill a long-standing hole at a extra descriptive point. It stands proud very essentially from present courses on KAM conception since it leads the reader via an obtainable account of the speculation and locations it in its right context in arithmetic, physics, and the heritage of science.

**Contents:**

- Introduction
- Minimum Mathematical Background
- Leading as much as KAM: A caricature of the History
- KAM Theory
- KAM in Context: Questions, outcomes, Significance
- Other leads to Hamiltonian Perturbation concept (HPT)
- Physical Applications
*Appendices:*
- Kolmogorov's 1954 Paper
- Overview of Low-Dimensional Small Divisor Problems
- East Meets West — Russians, Europeans, Americans
- Guide to extra Reading
- Selected Quotations
- Glossary

**Readership:** Undergraduates, graduates, and researchers largely attracted to Hamiltonian perturbation conception, statistical mechanics, ergodic concept, Nekhoroshev concept, Arnold diffusion, nonlinear dynamics, dynamical structures, chaos concept, classical mechanics, and the background of those subjects.