How the Minimal Poincaré Return Time Depends on the Size of a Return Region in a Linear Circle Map - Semenova, N.; Rybalova, E.; Anishchenko, V. (Discontinuity, Nonlinearity, and Complexity, 2026)
It is found that the step function of dependence of the minimal Poincaré return time on the size of a return region τinf(ε) for the linear circle map with an arbitrary rotation number can be approximated analytically. All analytical results are confirmed by numerical simulation.