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In the present work new analytical results for the 3-cycles of the logistic map are obtained.
We study internal structure of the Kemmer–Duffin–Petiau equations for spin-0 and spin-1 mesons. We demonstrate, that the Kemmer–Duffin–Petiau equations can be splitted into constituent equations, describing particles with definite mass and broken Lorentz symmetry. We also show that solutions of the three-component constituent equations fulfill the Dirac… (More)
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to the next impact, is derived. Periodic points are found and their stability is determined. The grazing manifold is… (More)
Non-invertible discrete-time dynamical systems can be derived from group actions. In the present work possibility of application of this method to systems of ordinary differential equations is studied. Invertible group actions are considered as possible candidates for stroboscopic maps of ordinary differential equations. It is shown that a map on SU (2)… (More)
In the present work we make a small step towards finding explicit formula for polynomial roots. Explicit formulae for simple real roots, based on the Frobenius companion matrix, are derived. After some modifications the method can be used to compute multiple or complex roots.
A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.