Periodic Behavior of Maps Obtained by Small Perturbations of Smooth Skew Products - Efremova, L.S. (Discontinuity, Nonlinearity, and Complexity, 2026)
We study C^1-smooth maps obtained by small perturbations of C^1-smooth skew products of maps of an interval with Ω-stable quotients and present results on the coexistence of periods of periodic orbits for maps under consideration. In particular, C^1-smooth Ω-stable maps of an interval do not contain maps of type 2^∞, i.e. maps that have the unbounded set of (the least) periods of periodic orbits τ for τ={2^i}_i≥ 0. We prove here that analogously to C^1-smooth skew products of maps of an interval with Ω-stable quotients there exist the maps under consideration with τ={2^i}_i≥ 0.