Mathematics · Complex Analysis
A Möbius transformation T(z) = az + bcz + d with ad - bc ≠ 0 is said to be hyperbolic if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It has two distinct fixed points and is conjugate to a rotation z ↦ eiθz with θ ≠ 2kπ
- 2It has no fixed points in the extended complex plane
- 3It has two distinct fixed points and is conjugate to a pure dilation z ↦ λz with λ > 0, λ ≠ 1✓
- 4It has exactly one fixed point of multiplicity two
Correct answer
It has two distinct fixed points and is conjugate to a pure dilation z ↦ λz with λ > 0, λ ≠ 1
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