Existence of stable orbits in the $x^{2}$ $y^{2}$ potential

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3 December 1990

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 65 (23) , 2837-2838
https://doi.org/10.1103/physrevlett.65.2837

Abstract

We have found the presence of at least one family of stable periodic orbits in the system H=1/2(

p_{x}^{2}

+

p_{y}^{2}

+

x^{2}

y^{2}

). This counterproves earlier claims that the

x^{2}

y^{2}

potential gives fully ergodic motion.

Keywords

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