2016
DOI: 10.1016/j.indag.2015.11.001
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Abstract: In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method incorporates validated truncation error bounds, and maximizes the size of the image of the polynomial approximation relative to some specified constraints. More precisely we use that the manifold computations depend heavily on the scalings of the eigenvectors: indeed we study the precise effects of these scalings on the estimates whi… Show more

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Cited by 34 publications
(91 citation statements)
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“…See [46] for a proof of this identity, and also the discussion in [25,27]. The coefficients of the rescaled parameterization have the new exponential decay rate given by…”
Section: Rescaling the Eigenvectorsmentioning
confidence: 98%
See 2 more Smart Citations
“…See [46] for a proof of this identity, and also the discussion in [25,27]. The coefficients of the rescaled parameterization have the new exponential decay rate given by…”
Section: Rescaling the Eigenvectorsmentioning
confidence: 98%
“…In fact the effect of rescaling the eigenvectors is made completely explicit as follows. The material in this section is discussed in greater detail in [46]. Suppose that…”
Section: Rescaling the Eigenvectorsmentioning
confidence: 99%
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“…For more detailed discussion see Breden et al (2015) and also Falcolini and de la Llave (1992) and Cabré et al (2003a).…”
Section: Non-resonant Eigenvaluesmentioning
confidence: 98%
“…Additionally and without loss of generality, we prescribe the linear constraints Breden et al (2015), Falcolini and de la Llave (1992) and Cabré et al (2003a) for a more thorough discussion of this topic.…”
Section: The Invariance Equationmentioning
confidence: 99%