Fatou conjecture

In mathematics, the Fatou conjecture, named after Pierre Fatou, states that a quadratic family of maps from the complex plane to itself is hyperbolic for an open dense set of parameters.

References

• Świątek, Grzegorz; Graczyk, Jacek (1998), The real Fatou conjecture, Annals of Mathematics Studies 144, Princeton University Press, ISBN 978-0-691-00257-6, MR 1657075, ISBN 978-0-691-00258-3