Poincaré maps of Duffing--type oscillators and their reduction to circle maps. I. Analytic results

G. Eilenberger, K. Schmidt

Bifurcation diagrams and plots of Lyapunov exponents in the $r$--$\Omega$ --plane for Duffing--type oscillators $$\ddot{x}+2r\dot{x}+V^{\prime }(x,\Omega t)=0$$ exhibit a regular pattern of repeating…