Geodesic
Analytic enclosure of the fundamental matrix solution
Applications of Mathematics, Tome 60 (2015) no. 6, pp. 617-636

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This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing the enclosure in the $C^s$ category.
DOI : 10.1007/s10492-015-0114-6
Classification : 34A05, 37B55, 65G99
Keywords: rigorous numerics; fundamental matrix solution; Floquet theory; analytical category 
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Castelli, Roberto; Lessard, Jean-Philippe; Mireles James, Jason D. Analytic enclosure of the fundamental matrix solution. Applications of Mathematics, Tome 60 (2015) no. 6, pp. 617-636. doi: 10.1007/s10492-015-0114-6

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