These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 36.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/1, 0/3, 0/9, 0/18, 0/36, 1/12, 1/6, 1/4, 1/3, 1/2, 2/4, 1/1, 2/2, 3/3
4/3, 7/3, 7/2, 4/1, 5/1, 7/1, 8/1, 13/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-2.016541)
(-1.983989,-1.058574)
(-0.945459,-0.669710)
(-0.663444,-0.503884)
(-0.495730,0.000000 )
( 0.000000,infinity )
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(-2.024390,-2.008000) -123/61 HST
(-2.016167,-1.984090) -2/1 EXTENDED HST
(-1.986278,-1.981733) -248/125 HST
(-1.106456,-0.912209) -1/1 EXTENDED HST
(-0.672727,-0.666667) -75/112 HST
(-0.668453,-0.664889) -2/3 EXTENDED HST
(-0.666667,-0.660377) -69/104 HST
(-0.505929,-0.501961) -65/129 HST
(-0.501997,-0.497987) -1/2 EXTENDED HST
(-0.498216,-0.493404) -59/119 HST
(-0.011213,0.011471 ) 0/1 EXTENDED HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
There are no slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 20768
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,a*c,a^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(33,34)(35,36)",
"c=<1,1,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"d=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,36)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(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)(33,34)(35,36)",
"b=<1,1,c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"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)(33,34)(35,36)",
"d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)(15,18)(17,20)(19,22)(21,24)(23,26)(25,28)(27,30)(29,32)(31,34)(33,36)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(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)(33,34)(35,36)",
"b=<1,1,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(33,34)(35,36)",
"d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)(15,18)(17,20)(19,22)(21,24)(23,26)(25,28)(27,30)(29,32)(31,34)(33,36)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,d*a,a^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"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)(33,34)(35,36)",
"c=<1,1,c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(32,33)(34,35)",
"d=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,36)",
"a*b*c*d");