These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 32.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/1, 0/8, 0/16, 0/32, 1/4, 1/2, 3/4, 1/1, 3/2, 4/2, 3/1, 4/1, 5/1, 7/1, 11/1
12/1, 13/1, 17/1, 27/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-6.466667,-2.017531)
(-1.980848,-1.000000)
(-1.000000,-0.500000)
(-0.500000,0.000000 )
( 0.000000,1.000000 )
( 1.000000,6.600000 )
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(-9.466667,-8.352941) -9/1 EXTENDED HST -> HST
(-9.391679,-7.556938) -25/3 EXTENDED HST -> HST
(-8.333333,-7.470588) -8/1 EXTENDED HST -> HST
(-8.148890,-6.752296) -22/3 EXTENDED HST -> HST
(-7.333333,-6.470588) -7/1 EXTENDED HST -> HST
(-6.900000,-6.088235) -110/17 HST
(-2.018206,-1.982119) -2/1 EXTENDED HST
(-1.991989,-1.970741) -105/53 HST
(-1.015873,-0.984615) -1/1 EXTENDED HST
(-0.506858,-0.493141) -1/2 EXTENDED HST
(-0.015384,0.015874 ) 0/1 EXTENDED HST
( 0.982119,1.018207 ) 1/1 EXTENDED HST
( 5.880197,7.550633 ) 20/3 EXTENDED HST -> HST
( 6.705882,7.600000 ) 7/1 EXTENDED HST -> HST
( 7.588235,8.733333 ) 8/1 EXTENDED HST -> HST
( 8.588235,9.733333 ) 9/1 EXTENDED HST -> HST
-9.237305)(9.238281 infinity EXTENDED HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
There are no slope function fixed points because every
loop multiplier of the mod 2 slope correspondence graph
is at least 1 and the map is rational.
No nontrivial cycles were found.
The slope function maps some slope to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50
and |q| <= 50 ends in the nonslope.
If the slope function maps slope p/q to slope p'/q', then |p'| <= |p|
for every slope p/q with |p| <= 50 and |q| <= 50.
If the slope function maps slope p/q to slope p'/q', then |q'| <= |q|
for every slope p/q with |p| <= 50 and |q| <= 50.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,b*c,d*a*c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"b=<1,1,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"d=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=<1,a^-1*c^-1,b^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"b=<1,1,c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"c=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"d=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=<1,a,c^-1*b*c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"c=<1,1,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"d=<1,a*c,a^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,1,b,b^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"b=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)",
"c=<1,1,c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"d=<1,d*a,a^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)",
"a*b*c*d");