Bifurcation locus

In complex dynamics, the bifurcation locus of a parameterized family of one-variable holomorphic functions informally is a locus of those parameterized points for which the dynamical behavior changes drastically under a small perturbation of the parameter. Thus the bifurcation locus can be thought of as an analog of the Julia set in parameter space. Without doubt, the most famous example of a bifurcation locus is the boundary of the Mandelbrot set. Parameters in the complement of the bifurcation locus are called J-stable.

## References

* Alexandre E. Eremenko and Mikhail Yu. Lyubich, Dynamical properties of some classes of entire functions, Annales de l'Institut Fourier 42 (1992), no. 4, 989-1020, http://www.numdam.org/item?id=AIF_1992__42_4_989_0.
* Mikhail Yu. Lyubich, Some typical properties of the dynamics of rational mappings (Russian), Uspekhi Mat. Nauk 38 (1983), no. 5(233), 197-198.
* Ricardo Mañé, Paulo Sad and Dennis Sullivan, On the dynamics of rational maps, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 2, 193-217, http://www.numdam.org/item?id=ASENS_1983_4_16_2_193_0.
* Curtis T. McMullen, Complex dynamics and renormalization, Annals of Mathematics Studies, 135, Princeton University Press, Princeton, NJ, 1994. ISBN 0-691-02982-2.

## See also

* Connectedness locus

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