Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called dendritic. By results of Kiwi, any dendritic polynomial is semiconjugate to a topological polynomial whose topological Julia set is a dendrite. We construct a continuous map of the space of all cubic dendritic polynomials onto a laminational model that is a quotient space of a subset of the closed bidisk. This construction generalizes the “pinched disk” model of the Mandelbrot set due to Douady and Thurston. It can be viewed as a step towards constructing a model of the cubic connectedness locus.
The present textbook is intended for students preparing to study mathematics at a higher education institution, to prepare to pass the exam.
The tasks and problems reflecting universality and beauty of the method of uncertain coefficients in a school course of algebra are considered in the article. The idea of the method will allow pupils to expand the ideas of operation with polynomials, to reveal another way of division of a polynomial into a polynomial, to acquire skills of disposal of irrationality in a fraction denominator, to learn to display the proper rational fraction into the elementary ones. The examples given in the article can be useful for both mathematics teachers, and the pupils who are seriously involved in mathematics.