Porosity of parabolic julia sets^∗

^∗Financially supported by “Studienstiftung des deutschen Volkes” and “Graduier-tenkolleg Stochastische Prozesse und probabilistische Analysis”

Abstract

It is proved that Julia sets of parabolic rational maps are porous This implies that the box counting dimension of these Julia sets is always strictly less than two, which was shown before by Aaronson Denker and Urbanski using conformal measures Our proof uses only elementary techniques from complex analysis and iteration of rational maps.

Keywords:

• Julia sets
• porosity
• dimension
• complex dynamics
• parabolic
• expansive
• rational maps

1991 Mathematics Subject Classification:

• Primary 30D05
• Secondary 58F23

^∗Financially supported by “Studienstiftung des deutschen Volkes” and “Graduier-tenkolleg Stochastische Prozesse und probabilistische Analysis”

^† [email protected]

^∗Financially supported by “Studienstiftung des deutschen Volkes” and “Graduier-tenkolleg Stochastische Prozesse und probabilistische Analysis”

^† [email protected]

Notes

^∗Financially supported by “Studienstiftung des deutschen Volkes” and “Graduier-tenkolleg Stochastische Prozesse und probabilistische Analysis”

^† [email protected]