Meaning of Möbius transformation | Babel Free

Definitions

A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.

Equivalents

Examples

“2008, J. Vernon Armitage, John Parker, Jørgensen's inequality for Non-Archimedean Metric Spaces, Mikhail Kapranov, Sergii Kolyada, Yu. I. Manin, Pieter Moree, Leonid Potyagailo (editors), Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov, page 97, Jørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete.”

“2012, Martin Delacourt, Petr Kůrka, Finite State Transducers of Modular Möbius Number⟳ Systems, Branislav Rovan, Vladimiro Sassone, Peter Widmayer (editors), Mathematical Foundations of Computer Science 2012, 37th International Symposium, MFCS 2012, Proceedings, Springer, LNCS 7464, page 323, Modular Möbius number⟳ systems consist⟳ of Möbius transformations with integer coefficients and unit determinant.”

“Classical Kleinian groups are discrete subgroups of Möbius transformations which act on the Riemann sphere with a nonempty region of discontinuity.”

CEFR level