| Abstract: |
| We discuss how the Arnold conjecture on $CP^n$ is equivalent to a certain bifurcation problem. Namely, we end up with a family $F_\lambda = L + K_\lambda: H \to H$ such that $L$ is a fixed Fredholm map, $K_\lambda$ is a nonlinear compact perturbation with $K_\lambda(0) = 0$ and $H$ is a separable Hilbert space. Since $K_\lambda$ may not be differentiable at $0$ we cannot use spectral flow (or comparison of Morse indicies) arguments to show existence of bifurcation. Therefore Conley index together with its relative cup-length will be briefly discussed. |
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