Abstract:
A. Klimenko, jointly with O. Romaskevich, obtained a result
concerning asymptotics of the Arnold tongues boundaries for a
two-parametric family of vector fileds
on a 2-torus. This family arises as a model describing effects emerging
in a Josephson contact under oscullating electromagnetic field. Namely,
it is shown that two boundaries of Arnold tongue corresponding to any
integer rotation number are analytical curves that have inifinitely many
intersections, and that these curves are asymptotically equivalent to
graphs of Bessel functions appropriately scaled and shifted. The method
developed for this problem is based on construction of Gronwall-type
inequalities; it can be applicable to similar problems.
References
A. Klimenko, O. Romaskevich, “Asymptotic properties of Arnold tongues and Josephson effect”, Moscow Math. J., 14:2 (2014), 367–384, arXiv: 1305.6746
