A-stabilization and the ranges of complex polynomials on the unit disk

2017/01/17 by Alexey Solyanik, Solyanik, Alexey
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1701.04784

openalex publication_date 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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) = q₁z + q₂z² +… + q_nzⁿ defined in the unit disk and normalized by the conditions q(1) = 1 and this is the main subject of the present paper.

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