A simple proof of Sullivan's complex bounds
Genadi Levin
TL;DR
This paper offers a straightforward and simplified proof of Sullivan's complex bounds, a key precompactness property for certain quadratic polynomials, originally proven over 35 years ago.
Contribution
The paper provides a new, simpler 'soft' proof of Sullivan's complex bounds for infinitely renormalizable quadratic polynomials with bounded combinatorics.
Findings
Simplified proof of Sullivan's complex bounds
Clarification of precompactness property for quadratic polynomials
Potential for easier understanding and further research
Abstract
About 35 years ago Dennis Sullivan proved a precompactness property ("complex bounds") for infinitely renormalizable real quadratic polynomials with bounded combinatorics. We present a simple "soft" proof of this remarkable result.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Holomorphic and Operator Theory · Meromorphic and Entire Functions