Spectral flow is a complete invariant for detecting bifurcation of critical points

  title={Spectral flow is a complete invariant for detecting bifurcation of critical points},
  author={James C. Alexander and Patrick M. Fitzpatrick},
  journal={Transactions of the American Mathematical Society},
Given a one-parameter path of equations for which there is a trivial branch of solutions, to determine the points on the branch from which there bifurcate nontrivial solutions, there is the heuristic principle of linearization. That is to say, at each point on the branch, linearize the equation, and justify the inference that points on the branch that are bifurcation points for the path of linearized equations are also bifurcation points for the original path of equations. In quite general… 
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