The topology of the monodromy map of the second order ODE
نویسندگان
چکیده
We consider the following question: given A ∈ SL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential q ∈ L2([0, 2π]) to μ(q) = Φ̃(2π), the lift to the universal cover G = ̃ SL(2,R) of SL(2,R) of the fundamental matrix map Φ : [0, 2π] → SL(2,R), Φ(0) = I, Φ(t) = (
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