On Littlewood’s Counterexample of Unbounded Motions in Superquadratic Potentials

  • Mark Levi
Chapter
Part of the Dynamics Reported book series (DYNAMICS, volume 1)

Abstract

Littlewood [11] constructed an example of an equation of the form ẍ + V’(t) with \( \frac{{V'(x)}}{x} \to \infty \) and yet possessing unbounded solutions. This note contains a considerable simplification of Littlewood's construction together with rather precise information on the behavior of \( \frac{{V'(x)}}{x} \to \infty \) under which the resonances of the type constructed by Littlewood are possible. The original construction [11] contained an error, as was pointed out by Yiming Long, who also corrected the original proof [12].

Keywords

Resonance Condition Unbounded Solution Twist Condition Piecewise Linear Continuous Function Middle Interval 
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© Springer-Verlag Berlin Heidelberg 1992

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  • Mark Levi

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