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Perturbed n-sphere theory

  1. Jul 12, 2011 #1
    Is anyone familiar with books or papers on perturbation theory for closed levels sets in which the equation for the n-sphere is perturbed? For example, the level set:

    [tex]\sum_{i=1}^n x_i^2 + \epsilon p(x_i) = C[/tex]

    where [tex]\epsilon[/tex] is a small parameter and [tex]p(x_i)[/tex] is a positive polynomial such as [tex]x_i^4[/tex].
  2. jcsd
  3. Jul 12, 2011 #2
    In particular, say [tex]A(C,\epsilon)[/tex] is the "surface area". Then we can expand it:

    [tex]A(C,\epsilon) = A(C,0) + \epsilon (dA/d\epsilon)(C,0) + \dots[/tex]

    How do I figure out what [tex](d^nA/d\epsilon^n)(C,0)[/tex] is from the equation for the level set?
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