Global attractor in quasi-periodically forced Josephson junctions (Q2752322)

The author deals with the global dynamics of the equation NEWLINE\[NEWLINE \ddot\phi+\beta\dot\phi+\sin\phi=\gamma F(\omega_1 t,\omega_2 t,\dots,\omega_N t) , NEWLINE\]NEWLINE where \(\beta\), \(\gamma\) are constants, \(\beta>0\), \(\omega_1,\omega_2,\dots,\omega_N\) are real rationally independent numbers, \(F\) is a continuous \(2\pi\)-periodic function in each variable and \(|F|\leq 1\). This equation arises in physical problems as charge density waves, Josephson junction and damped pendulum, where \(F\) denotes the forcing. The dynamics is studied when \(\beta\) is not small. Similar to the periodic case (N=1), it is proved that when \(\beta>0\) the equation has a one-dimensional global attractor. It is shown that under certain condition the dynamics on the global attractor is not chaotic and residually many orbits are almost automorphic.