Discontinuity, Nonlinearity, and Complexity
Periodic Behavior of Maps Obtained by Small Perturbations of Smooth Skew Products
Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 519523  DOI:10.5890/DNC.2020.12.004
L.S. Efremova
Institute of Information Technologies, Mathematics and Mechanics, Nizhni Novgorod State University,
Nizhni Novgorod, 603950, Russia
Department of General Mathematics,
Moscow Institute of Physics and Technology,
Moscow Region, Dolgoprudny, 141701, Russia
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Abstract
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 $\tau=\{2^i\}_{i\geq 0}.$
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