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Cited by 18 publications
(24 citation statements)
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“…The following proposition sums up what has been proven up to now in this section, namely that we have derived bounds that satisfy the requirements (11) to (14) from Theorem 3.5.…”
Section: The Radii Polynomials and Interval Arithmeticsmentioning
confidence: 60%
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“…The following proposition sums up what has been proven up to now in this section, namely that we have derived bounds that satisfy the requirements (11) to (14) from Theorem 3.5.…”
Section: The Radii Polynomials and Interval Arithmeticsmentioning
confidence: 60%
“…In the next section, we show how to obtain bounds Y and Z satisfying (11)- (14). Before doing so, let us make a quick remark about the different representations and norms we can use on X n m,k .…”
Section: Back To a Fixed Point Formulationmentioning
confidence: 99%
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“…Validated numerics for stable/unstable manifolds based on functional analytic tools are discussed at length below, and for the moment we only mention the work of Koch and Arioli [51,52] on homoclinic connecting orbits traveling waves, and the Evans function; and also the work of the Breden, Lessard, Reinhardt, and the author on validated numerical methods for stable/unstable manifolds based on the parameterization method [53,54]. Techniques based on the parameterization method lead also to validated numerics for stable/unstable manifolds of periodic orbits, as in the work of Castelli, Lessard and the author [55], and also to validated numerical methods for computing unstable manifolds and heteroclinic connecting orbits for parabolic PDEs [56]. Further discussion of the literature is found in these references.…”
Section: A Brief Survey Of the Surrounding Literaturementioning
confidence: 99%
“…Then the methods of the work just cited apply directly to the expansions used in the present work. The key to the analysis in [Castelli et al, 2017] is that the approximation P N have small defect. In the present work we only check the defect numerically, and postpone to an upcoming work more careful analysis of the errors for our Chebyshev-Taylor approximations.…”
Section: Formal Series and The Reduction To Homological Equationsmentioning
confidence: 99%