A MASLOV INDEX FOR NON-HAMILTONIAN SYSTEMS

The candidate solution reproduces the structure and logic of Theorem 4.1 in the paper “A Maslov Index for Non-Hamiltonian Systems,” including: (i) the energy estimate guaranteeing λ∞ and absence of intersections on the top edge (Lemma 4.6) ; (ii) the small-δ argument removing left-edge intersections (Lemma 4.7) ; (iii) the rectangular homotopy identity equating the Maslov indices on the right and bottom edges (equation (39)) ; and (iv) the choice of hyperplanes H1,H2 and the derivative identity that makes all conjugate-point crossings positive (Lemma 4.8 using (26) and (32)) . The final inequality relating the number of nonnegative eigenvalues to conjugate points matches (20)–(22) in the paper . Minor stylistic differences (e.g., use of Θs vs. a direct bound on the Robin boundary term) do not affect correctness.