Geodesic
Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 148-171

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We study conditions for the hyperbolicity of periodic solutions to nonlinear functional differential equations in terms of the eigenvalues of the monodromy operator. The eigenvalue problem for the monodromy operator is reduced to a boundary value problem for a system of ordinary differential equations with a spectral parameter. This makes it possible to construct a characteristic function. We prove that the zeros of this function coincide with the eigenvalues of the monodromy operator and, under certain additional conditions, the multiplicity of a zero of the characteristic function coincides with the algebraic multiplicity of the corresponding eigenvalue. 
@article{TM_2007_256_a7,
     author = {N. B. Zhuravlev and A. L. Skubachevskii},
     title = {Hyperbolicity of {Periodic} {Solutions} of {Functional} {Differential} {Equations} with {Several} {Delays}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {148--171},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_256_a7/}
}
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N. B. Zhuravlev; A. L. Skubachevskii. Hyperbolicity of Periodic Solutions of Functional Differential Equations with Several Delays. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 148-171. http://geodesic.mathdoc.fr/item/TM_2007_256_a7/