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Parabolic perturbation of the family \(\lambda\tan z\). (English) Zbl 1101.30026
Devaney, Robert L. (ed.) et al., Complex dynamics. Twenty-five years after the appearance of the Mandelbrot set. Proceedings of an AMS-IMS-SIAM joint summer research conference, Snowbird, UT, USA, June 13–17, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3625-0/pbk). Contemporary Mathematics 396, 115-128 (2006).
The authors study parabolic bifurcation in holomorphic dynamics. They also apply their result to the family \(\lambda \tan z\) to complete the proof that there are infinite cascades of non-standard period doubling bifurcation along the imaginary axis.
For the entire collection see [Zbl 1084.37002].

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
30F30 Differentials on Riemann surfaces
37E35 Flows on surfaces
52C26 Circle packings and discrete conformal geometry