Length of the Instability Intervals for Hill's Equation

Malik Mamode (1)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

The length of instability intervals is investigated for the Hill equation y′′+ω(ω− 2∈p(x)y = 0, where p(x) has an infinite Fourier series of coefficients cn. For any small ∈ it is shown that these lengths are completely characterized by the cn's.

Mots clés: Hill equation; discriminant; instability interval

Domaines: Physique mathématique [math-ph]

Malik Mamode. Length of the Instability Intervals for Hill's Equation. Letters in Mathematical Physics, 2004, 67 (2), pp.95-102. ⟨10.1023/B:MATH.0000032748.69047.08⟩. ⟨hal-01171489⟩