Periodic Behavior of Maps Obtained by Small Perturbations of Smooth Skew Products
DOI:
https://doi.org/10.5890/DNC.2020.12.004Abstract
We study $C^1$-smooth maps obtained by small perturbations of $C^1$-smooth skew products of maps of an interval with $\Omega$-stable quotients and present results on the coexistence of periods of periodic orbits for maps under consideration. In particular, $C^1$-smooth $\Omega$-stable maps of an interval do not contain maps of type $2^{\infty}$, i.e. maps that have the unbounded set of (the least) periods of periodic orbits $\tau$ for $\tau=\{2^i\}_{i\geq 0}$. We prove here that analogously to $C^1$-smooth skew products of maps of an interval with $\Omega$-stable quotients there exist the maps under consideration with $\tau=\{2^i\}_{i\geq 0}.$References
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