Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets

2005/06/08 by Peter Makienko, Makienko, Peter
Mathematics · #37F10 #37F30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37F10 #msc:37F30

paper · pdf · doi:10.48550/arxiv.math/0506141

arxiv created 2005/06/08 · arxiv updated 2009/12/01

Abstract

Let R be a rational map with totally disconnected Julia set J(R). If the postcritical set on J(R) contains a non-persistently recurrent (or conical) point, then we show that the map R can not be a structurally stable map.

Related

• Non-recurrent rational maps with disconnected Julia set
• Decomposition of rational maps by stable multicurves
• Invariant graphs in Julia sets and decompositions of rational maps
• Renormalization and wandering continua of rational maps
• Renormalizations and wandering Jordan curves of rational maps