In section 49 (and 50) of Landau and Lifschitz's "Classical Mechanics", adiabatic invariants are discussed, which are related to functions which vary adiabatically or "slowly" with time.

Admittedly the book is a translation from Russian, but is "slowly varying" in the sense meant in this book, the same as in the sense defined by Karamata?

Or is it just meant in the book as a vague, ill-defined heuristic?

I wonder since slowly-varying functions in the sense of Karamata have surprisingly many applications to probability theory, and I was wondering if this constituted a connection between classical mechanics and probability theory via slowly varying functions.

  • $\begingroup$ Landau-Lifshitz is a beginner's book in mechanics, so it only sketches out broad ideas, but if you want to do Hamiltonian perturbation theory correctly (do you, really????), then you have to read texts that are a lot deeper and a lot more precise (and a lot less fun to read). $\endgroup$
    – CuriousOne
    May 5, 2016 at 10:59
  • $\begingroup$ What does this have to do with Hamiltonian perturbation theory? I don't understand. $\endgroup$ May 19, 2016 at 14:20
  • $\begingroup$ I just want to know what the correct definition of "slowly varying function" is within the context of adiabatic invariant -- the answer should be a one-liner, not a whole textbook. Now if I want to understand why that choice of definition is useful/makes sense, then I would bother to read a whole textbook about it. But first things first please. $\endgroup$ May 19, 2016 at 14:21


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