def Hilion_parabolic(k=1):
"""
Automorphism given in Section 2 of [Hilion].
This automorphism has a parabolic orbit inside F_4.
REFERENCES:
[Hilion] A. Hilion
"""
F=FreeGroup(4)
phi=FreeGroupAutomorphism("a->a,b->ba,c->caa,d->dc",F)
if k>1:
phi=phi*pow(F.dehn_twist(c,a),k-1)
return phi
def Hilion_parabolic(k=1):
"""
Automorphism given in Section 2 of [Hilion].
This automorphism has a parabolic orbit inside F_4.
REFERENCES:
[Hilion] A. Hilion, Dynamique des automorphismes des groupes
libres, Thesis (Toulouse, 2004).
"""
F=FreeGroup(4)
phi=FreeGroupAutomorphism("a->a,b->ba,c->caa,d->dc",F)
if k>1:
phi=phi*pow(F.dehn_twist(c,a),k-1)
return phi
def Hilion_parabolic(k=1):
"""
Automorphism given in Section 2 of [Hilion].
This automorphism has a parabolic orbit inside F_4.
REFERENCES:
[Hilion] A. Hilion, Dynamique des automorphismes des groupes
libres, Thesis (Toulouse, 2004).
"""
F = FreeGroup(4)
phi = FreeGroupAutomorphism("a->a,b->ba,c->caa,d->dc", F)
if k > 1:
phi = phi * pow(F.dehn_twist(c, a), k - 1)
return phi
