Abstract:
Hill equation is considered. After transition to polar coordinates differential equation on torus for polar corner, satisfying to Karateodori conditions is gained. We shall give basic results.
Hill equation (with various multiplicators) is strongly stable (strongly unstable) then and only then, when the rotation number is nonintegral (integral) nonnegative number.
Formula connecting the nonintegral rotation number with multiplicators of Hill equation is received.
Keywords:strong stability, differential equations on torus, the number of rotation, multiplicators.
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