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Title: Stimulating
Review: Like his books on classical mechanics, a book that theoretical physicists should read. Unfortunately, the discussion of local integrability is too abstract and there is no distinction made with global integrability. Also irritating: because of a singularity at the origin the damped harmonic oscillator is not recognized as integrable in spite of the existence of a global conservation law, excepting one point in phase space. Integrability is an extremely difficult subject and maybe Arnol'd could have taught us more about it. I've discussed integrability/nonintegrability from a physicist's perspective in my Classical Mechanics (Cambridge, 1997).
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