Geodesic
Explicit solution family for the equation of the resistively shunted Josephson junction model
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 163-188 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain and study a family of solutions of the equation $\dot\phi+\sin\phi =B+A\cos\omega t$, which is applicable to several problems in physics, mechanics, and geometry. We use polynomial solutions of double confluent Heun equations associated with this equation to construct the family. We describe the manifold $M_{\mathrm P}$ of parameters $(A,B,\omega)$ of these solutions and obtain explicit formulas for the rotation number and Poincaré map of the dynamical system on a torus corresponding to this equation with parameters $(A,B,\omega)\in M_{\mathrm rP}$.
Keywords: dynamical system on a torus, rotation number
Mots-clés : double confluent Heun equations, polynomial solution, Poincaré map. 
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V. M. Buchstaber; S. I. Tertychnyi. Explicit solution family for the equation of the resistively shunted Josephson junction model. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 163-188. http://geodesic.mathdoc.fr/item/TMF_2013_176_2_a0/

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