1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook