These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 37.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/1, 0/37, 1/37, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1
12/1, 13/1, 14/1, 16/1, 17/1, 19/1, 25/1, 31/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-2.018515)
(-1.971840,-1.336882)
(-1.333168,-1.017349)
(-0.983233,-0.800059)
(-0.797976,-0.670767)
(-0.663676,-0.572646)
(-0.570313,-0.556134)
(-0.555033,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
(-2.023798,-2.011951) -111/55 HST
(-2.015850,-2.007975) -169/84 HST
(-2.008926,-1.991153) -2/1 EXTENDED HST
(-1.995693,-1.979407) -161/81 HST
(-1.987532,-1.975467) -107/54 HST
(-1.981270,-1.963257) -71/36 HST
(-1.338981,-1.334496) -127/95 HST
(-1.335311,-1.331361) -4/3 EXTENDED HST
(-1.196696,-0.858778) -1/1 EXTENDED HST
(-0.800712,-0.799290) -4/5 EXTENDED HST
(-0.799971,-0.795766) -79/99 HST
(-0.672079,-0.669390) -55/82 HST
(-0.670243,-0.668469) -83/124 HST
(-0.669000,-0.667843) -125/187 HST
(-0.668216,-0.667449) -191/286 HST
(-0.667656,-0.665681) -2/3 EXTENDED HST
(-0.667906,-0.659256) -75/113 HST
(-0.572953,-0.572205) -71/124 HST
(-0.572650,-0.571680) -107/187 HST
(-0.571792,-0.571066) -4/7 EXTENDED HST
(-0.571263,-0.570629) -169/296 HST
(-0.570946,-0.570467) -113/198 HST
(-0.570682,-0.569940) -77/135 HST
(-0.556780,-0.555470) -109/196 HST
(-0.555830,-0.555281) -5/9 EXTENDED HST
(-0.555465,-0.554628) -121/218 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.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,a*c,a^-1,1,c^-1*b*c,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)",
"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>(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,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)",
"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)(34,37)",
"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,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)(32,33)(34,35)(36,37)",
"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)(35,37)",
"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,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)",
"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>(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)(35,37)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,d*a,a^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)",
"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,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)(32,33)(34,35)(36,37)",
"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)(34,37)",
"a*b*c*d");