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• W4384024762 abstract "To investigate the degree <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> connectedness locus, Thurston [<italic>On the geometry and dynamics of iterated rational maps</italic>, Complex Dynamics, A K Peters, Wellesley, MA, 2009, pp. 3–137] studied <italic><inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma Subscript d> <mml:semantics> <mml:msub> <mml:mi>σ<!-- σ --></mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>sigma _d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-invariant laminations</italic>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma Subscript d> <mml:semantics> <mml:msub> <mml:mi>σ<!-- σ --></mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>sigma _d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-tupling map on the unit circle, and built a topological model for the space of quadratic polynomials <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f left-parenthesis z right-parenthesis equals z squared plus c> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>f(z) = z^2 +c</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In the spirit of Thurston’s work, we consider the space of all <italic>cubic symmetric polynomials</italic> <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Subscript lamda Baseline left-parenthesis z right-parenthesis equals z cubed plus lamda squared z> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>λ<!-- λ --></mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>λ<!-- λ --></mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>z</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>f_lambda (z)=z^3+lambda ^2 z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a series of three articles. In the present paper, the first in the series, we construct a lamination <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Subscript s Baseline upper C upper L> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>C</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>C_sCL</mml:annotation> </mml:semantics> </mml:math> </inline-formula> together with the induced factor space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper S slash upper C Subscript s Baseline upper C upper L> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>C</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb {S}/C_sCL</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the unit circle <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper S> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb {S}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. As will be verified in the third paper of the series, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper S slash upper C Subscript s Baseline upper C upper L> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>C</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb {S}/C_sCL</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a monotone model of the <italic>cubic symmetric connectedness locus</italic>, i.e. the space of all cubic symmetric polynomials with connected Julia sets." @default.
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• W4384024762 date "2023-07-12" @default.
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• W4384024762 title "Symmetric cubic laminations" @default.
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