Limit drift for complex Feigenbaum mappings

Genadi Levin, Grzegorz Świątek

Research output: Contribution to journalArticlepeer-review

Abstract

We study the dynamics of towers defined by fixed points of renormalization for Feigenbaum polynomials in the complex plane with varying order of the critical point. It is known that the measure of the Julia set of the Feigenbaum polynomial is positive if and only if almost every point tends to under the dynamics of the tower for corresponding. That in turn depends on the sign of a quantity called the drift. We prove the existence and key properties of absolutely continuous invariant measures for tower dynamics as well as their convergence when tends to. We also prove the convergence of the drifts to a finite limit, which can be expressed purely in terms of the limiting tower, which corresponds to a Feigenbaum map with a flat critical point.

Original languageAmerican English
Pages (from-to)2428-2479
Number of pages52
JournalErgodic Theory and Dynamical Systems
Volume41
Issue number8
DOIs
StatePublished - Aug 2021

Keywords

  • Feigenbaum function
  • invariant measure
  • limit drift
  • measure of Julia set

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics

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