 Arnold Diffusion by Variational MethodsJohn N. Mather ()
A chapter in Essays in Mathematics and its Applications, 2012, pp 271-285 from Springer Abstract: Abstract In this paper, we correct results announced in Mather (J Math Sci NY 124:5275–5289, 2003) and make some observations on the proofs of these results. The principal result, Theorem 1, is a strong form of Arnold diffusion in two and one half degrees of freedom, under suitable genericity hypotheses. After (Mather, J Math Sci NY 124:5275–5289, 2003) appeared, we realized that there is an oversight in our planned proof. Because of the oversight, the genericity conditions that we imposed on U in Mather (J Math Sci NY 124:5275–5289, 2003) are not enough. In this paper, we state further genericity conditions, which are enough for our revised proof. In addition, we note that a slightly stronger differentiability hypothesis than we stated in Mather (J Math Sci NY 124:5275–5289, 2003) is needed. In the later sections of this paper, we make some observations related to the proof of Theorem 1. The complete (revised) proof will appear elsewhere. Keywords: Quadratic Form; Global Minimum; Rotation Vector; Small Denominator; Positive Definite Quadratic Form (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_11 Ordering information: This item can be ordered from DOI: 10.1007/978-3-642-28821-0_11 Access Statistics for this chapter More chapters in Springer Books from Springer |
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