arXiv subjects
Publications and source records attributed to Alexey Solyanik.
In this note, we use a toy problem of detecting cycles of length two in a tent map to highlight some curious phenomena in the behavior of discrete dynamical systems. This work presents no new results or proofs, only computer experiments and illustrations. Thus, it serves as light reading and does not aim to be a scientific paper but is rather educational in nature. For this reason it is accompanied by numerous illustrations.
Problems of stabilization of the unstable cycle of one-dimensional complex dynamical system are briefly discussed. These questions reduced to the problem of description of the ranges of polynomials $q(z) = q_1z + q_2z^2 +\dots + q_nz^n$ defined in the unit disk and normalized by the conditions $q(1) = 1 $ and this is the main subject of the present paper.
We present one of the approaches to find the best approximation of the given function by trigonometric polynomials in $L^1$ metric and applied it to find the optimal constants in the Nikolsky's type inequality, concerning approximation of Lipschitz functions by algebraic polynomials.
In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials