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.
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Dedicated to the 80th Anniversary of Professor Stephen Smale
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© 2012 Springer-Verlag Berlin Heidelberg
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Mather, J.N. (2012). Arnold Diffusion by Variational Methods. In: Pardalos, P., Rassias, T. (eds) Essays in Mathematics and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28821-0_11
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DOI: https://doi.org/10.1007/978-3-642-28821-0_11
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