Misiurewicz maps unfold generically (even if they are critically non-finite)

Sebastian van Strien
2000 Fundamenta Mathematicae  
We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if f λ 0 is critically finite with non-degenerate critical point c 1 (λ 0 ), . . . , cn(λ 0 ) such that f k i λ 0 (c i (λ 0 )) = p i (λ 0 ) are hyperbolic periodic points for i = 1, . . . , n, then is a local diffeomorphism for λ near λ 0 . For quadratic families this result was proved previously in [DH] using entirely different methods.
doi:10.4064/fm-163-1-39-54 fatcat:rj36527ejbbtlnmufh3jriyr4m