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From the paper cited below:
“In Table 1 the following Sharkovskiy’s series is shown 3; 5; 22 ⋅5; 9 . It should be emphasized that the so called Sharkovskiy’s series is not followed from each other, but they should be separated from the parameters {q0,ω0} space. The following scenarios are detected: In the case of period
tripling a partition to three equal parts of the signal is observed; for period 5 we deal with 5 equal parts, and so on. In Poincaré maps one observes 3; 5; 22 ⋅5; 9 points. In a phase portrait period doubling is observed too. The mentioned orbits are situated in the windows of regularity occurred in chaos and their structure is the same in the whole studied manifold.”
This image is from:
Vadim A. Krysko, Jan Awrejcewicz, Natalya E. Saveleva and Anton C. Krysko,
“On the Sharkovskiy’s periodicity for differential equations governing dynamics of flexible shells”, Eighth Conference on Dynamical Systems Theory and Applications, December 12-15, 2005, Lodz, Poland
ABSTRACT: In this work complex vibration of flexible elastic shells subjected to transversal and sign changeable local load in the frame of non-linear classical theory are studied. A transition from partial to ordinary differential equations is carried out using the higher order Bubnov-Galerkin approach. Numerical analysis is performed applying theoretical background of nonlinear dynamics and qualitative theory of differential equations. Mainly the so called Sharkovskiy’s periodicity is studied.
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