Real cubic polynomials with a fixed point of multiplicity two

Autor:	Monireh Akbari, Maryam Rabii
Rok vydání:	2015
Předmět:	Combinatorics Discrete mathematics General Mathematics Chaotic Multiplicity (mathematics) Parameter space Invariant (mathematics) Fixed point Schwarzian derivative Cubic function Mathematics Conjugate
Zdroj:	Indagationes Mathematicae. 26:64-74
ISSN:	0019-3577
DOI:	10.1016/j.indag.2014.06.001
Popis:	The aim of this paper is to study the dynamics of the real cubic polynomials that have a fixed point of multiplicity two. Such polynomials are conjugate to f a ( x ) = a x 2 ( x − 1 ) + x , a ≠ 0 . We will show that when a > 0 and x ≠ 1 , then | f a n ( x ) | converges to 0 or ∞ and, if a 0 and a belongs to a special subset of the parameter space, then there is a closed invariant subset Λ a of R on which f a is chaotic.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5d79fa751816ef9677e86c29864f8a62 https://doi.org/10.1016/j.indag.2014.06.001 Zobrazit plný text záznamu Full Text from ScienceDirect