Symmetric cubic laminations

To investigate the degree d d connectedness locus, Thurston [On geometry and dynamics of iterated rational maps, Complex Dynamics, A K Peters, Wellesley, MA, 2009, pp. 3–137] studied σ encoding="application/x-tex">\sigma _d -invariant laminations, where is -tupling map on unit circle, built a topological model for space quadratic polynomials alttext="f left-parenthesis z right-parenthesis equals squared plus c"> f ( z stretchy="false">) = 2 + c encoding="application/x-tex">f(z) = z^2 +c . In spirit Thurston’s work, we consider all cubic symmetric polynomials lamda Baseline cubed z"> λ<!-- λ <mml:mn>3 encoding="application/x-tex">f_\lambda (z)=z^3+\lambda ^2 z in series three articles. present paper, first series, construct lamination alttext="upper C s upper L"> C s L encoding="application/x-tex">C_sCL together with induced factor alttext="double-struck S slash S / encoding="application/x-tex">\mathbb {S}/C_sCL circle S"> {S} As will be verified third paper monotone locus, i.e. cubic connected Julia sets.