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 $τ=\{2^i\}_{i≥ 0}.$