Abstract
We will describe recent developments in several intimately related problems of complex and real one-dimensional dynamics: rigidity of polynomials and local connectivity of the Mandelbrot set, measure of Julia sets, and attractors of quasi-quadratic maps. A combinatorial basis for this study is provided by the Yoccoz puzzle. The main problem is to understand the geometry of the puzzle. Our main geometric result is that in the quadratic case its principal moduli grow linearly. Renormalization ideas are strongly involved in the discussion. The interplay between real and complex dynamics enlightens both. In the end we will brieftly discuss a new geometric object which can be associated to a rational function, a hyperbolic orbifold 3-lamination.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
