The size of Mandelbrot bulbs

Author: 

Fowler, A
McGuinness, M

Publication Date: 

9 December 2019

Journal: 

Chaos, Solitons and Fractals

Last Updated: 

2021-10-10T18:47:25.927+01:00

Issue: 

September 2019

Volume: 

3

DOI: 

10.1016/j.csfx.2019.100019

page: 

100019-100019

abstract: 

We provide an analytic estimate for the size of the bulbs adjoining the main cardioid of the Mandelbrot set. The bulbs are approximate circles, and are associated with the stability regions in the complex parameter µ-space of period-q orbits of the underlying map z → z 2 − µ. For the (p, q) orbit with winding number p/q, the associated stability bulb is an approximate circle with radius 1q2 sin πpq.

Symplectic id: 

1076743

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article