Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

DOI to cite this document:: 10.5283/epub.1656

Brack, Matthias ; Fedotkin, Sergey ; Magner, Aleksandr ; Mehta, Mitaxi

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Date of publication of this fulltext: 05 Aug 2009 13:30

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Abstract

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lame functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an ...