Generic simple-spectrum conjecture for heteroclinic orbits

Let $H(t)$ denote the operator whose eigenvalues are considered along a heteroclinic orbit $u$ of

. **Generic simple-spectrum conjecture.** There is a generic \subset, in the Baire sense, of choices of the coefficients $a_i$ in

such that, for every heteroclinic orbit $u$, all eigenvalues of $H(t)$ are simple. This generic spectral property is part of the proposed framework for constructing connecting manifolds and Floer homology, but remains conjectural in the source.