Abstract
On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations. For suitable choices of the parameters, the Lorenz ODEs possess (i) stable and unstable manifolds of the stationary point 0 at the origin, (ii) a homoclinic orbit of 0, and (iii) a heteroclinic orbit connecting a periodic orbit with 0. With the exception of only partial results regarding (iii), all addressed orbits are enclosed and verified as follows: (a) enclosures of truncated series expansions and of their remainder terms yield guaranteed starting intervals at some distance from 0, whose width is not more than two units of the last mantissa digit, and (b) a step-size controlled version of Lohner’s enclosure algorithm for IVPs yields the continuations.
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Dedicated to Professor U. Kulisch on the occasion of his 60th birthday
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© 1993 Springer-Verlag
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Spreuer, H., Adams, E. (1993). On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations. In: Albrecht, R., Alefeld, G., Stetter, H.J. (eds) Validation Numerics. Computing Supplementum, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6918-6_17
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DOI: https://doi.org/10.1007/978-3-7091-6918-6_17
Publisher Name: Springer, Vienna
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