Geometry of $Q$-recurrent maps

Rodrigo A. Pérez

Geometry of $Q$-recurrent maps

动力系统 2007-05-23 v1

作者: Rodrigo A. Pérez

摘要

Given a critically periodic quadratic map with no secondary renormalizations, we introduce the notion of $Q$ -recurrent quadratic polynomials. We show that the pieces of the principal nest of a $Q$ -recurrent map $f_c$ converge in shape to the Julia set of $Q$ . We use this fact to compute analytic invariants of the nest of $f_c$ , to give a complete characterization of complex quadratic Fibonacci maps and to obtain a new auto-similarity result on the Mandelbrot set.

关键词

julia set thurston maps q-series and q-analogues

引用

@article{arxiv.math/0311359,
  title  = {Geometry of $Q$-recurrent maps},
  author = {Rodrigo A. Pérez},
  journal= {arXiv preprint arXiv:math/0311359},
  year   = {2007}
}

备注

8 figures

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