Skip to main content Accessibility help
×
Home

Sierpinski-curve Julia sets and singular perturbations of complex polynomials

  • PAUL BLANCHARD (a1), ROBERT L. DEVANEY (a1), DANIEL M. LOOK (a1), PRADIPTA SEAL (a1) and YAKOV SHAPIRO (a1)...

Abstract

In this paper we consider the family of rational maps of the complex plane given by \[z^2+\frac{\lambda}{z^2}\] where $\lambda$ is a complex parameter. We regard this family as a singular perturbation of the simple function $z^2$. We show that, in any neighborhood of the origin in the parameter plane, there are infinitely many open sets of parameters for which the Julia sets of the corresponding maps are Sierpinski curves. Hence all of these Julia sets are homeomorphic. However, we also show that parameters corresponding to different open sets have dynamics that are not conjugate.

Copyright

Sierpinski-curve Julia sets and singular perturbations of complex polynomials

  • PAUL BLANCHARD (a1), ROBERT L. DEVANEY (a1), DANIEL M. LOOK (a1), PRADIPTA SEAL (a1) and YAKOV SHAPIRO (a1)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed