2022/01/27 by Blokh, Alexander, Oversteegen, Lex, Selinger, Nikita +2
#37F50 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F20 #Secondary 37F10
paper · doi:10.48550/arxiv.2201.11434
To investigate the degree d connectedness locus, Thur\-ston studied σd-invariant laminations, where σd is the d-tupling map on the unit circle, and built a topological model for the space of quadratic polynomials f(z) = z2 +c. In the spirit of Thurston's work, we consider the space of all cubic symmetric polynomials fλ(z)=z3+λ2 z in a series of three articles. In the present paper, the first in the series, we construct a lamination CsCL together with the induced factor space \mathbbS/CsCL of the unit circle \mathbbS. As will be verified in the third paper of the series, \mathbbS/CsCL is a monotone model of the cubic symmetric connected locus, i.e. the space of all cubic symmetric polynomials with connected Julia sets.