Möbius transformations are the automorphisms of the Riemann sphere ℂ∪{∞}.
Every such map sends circles (and lines) to circles (and lines).
Fixed points: —
Type: —
tr² = (a+d)²
elliptic: tr²∈[0,4)
parabolic: tr²=4
hyperbolic: tr²>4
loxodromic: tr²∈ℂ\ℝ
Every such map sends circles (and lines) to circles (and lines).
Fixed points: —
Type: —
tr² = (a+d)²
elliptic: tr²∈[0,4)
parabolic: tr²=4
hyperbolic: tr²>4
loxodromic: tr²∈ℂ\ℝ