Yankl Mazor

Yankl Mazor

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

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Posts

Density of powers

1 minute read

Published:

Problem: Show that for almost every $x>1$ that {$x^k\mod 1$} is dense in $[0,1]$.

The Fatou-Sullivan Dictionary

4 minute read

Published:

(A lot of this table/post was written quickly and needs reorganization/explanation/citations.)

Cantor Sets I: Some Topology

3 minute read

Published:

I want to do some posts on my favorite topological space, the Cantor set. Cantor sets serve as important examples in virtually all fields of anlaysis and dynamical systems, as well as in geometric group theory and foliation theory. In this post I will describe some basic topological properties of Cantor sets, and in a following post I will describe some group actions on cantor sets.

Test Post

less than 1 minute read

Published:

This should be a heading

portfolio

publications

Antiholomorphic correspondences and mating I: realization theorems

Published in Communications of the AMS, 2024

In this paper, we study the dynamics of a general class of antiholomorphic correspondences; i.e., multi-valued maps with antiholomorphic local branches, on the Riemann sphere. Such correspondences are closely related to a class of single-valued antiholomorphic maps in one complex variable; namely, Schwarz reflection maps of simply connected quadrature domains. Using this connection, we prove that matings of all parabolic antiholomorphic rational maps with connected Julia sets (of arbitrary degree) and antiholomorphic analogues of Hecke groups can be realized as such correspondences. We also draw the same conclusion when parabolic maps are replaced with critically non-recurrent antiholomorphic polynomials with connected Julia sets.

Recommended citation: M. Lyubich, J. Mazor, S. Mukherjee. (2024). " Antiholomorphic correspondences and mating I: realization theorems." Comm. of the AMS 4 (2024), 495-547. https://www.ams.org/journals/cams/2024-04-11/S2692-3688-2024-00037-8/

Antiholomorphic correspondences and mating II: Shabat polynomial slices

Published in Arxiv, 2025

We study natural one-parameter families of antiholomorphic correspondences arising from univalent restrictions of Shabat polynomials, indexed by rooted dessin d’enfants. We prove that the parameter spaces are topological quadrilaterals, giving a partial description of the univalency loci for the uniformizing Shabat polynomials. We show that the escape loci of our parameter spaces are naturally (real-analytically) uniformized by disks. We proceed with designing a puzzle structure (dual to the indexing dessin) for non-renormalizable maps, yielding combinatorial rigidity in these classes. Then we develop a renormalization theory for pinched (anti-)polynomial-like maps in order to describe all combinatorial Multibrot and Multicorn copies contained in our connectedness loci (a curious feature of these parameter spaces is the presence of multiple period one copies). Finally, we construct locally connected combinatorial models for the connectedness loci into which the indexing dessins naturally embed.

Recommended citation: M. Lyubich, J. Mazor, S. Mukherjee. (2024). " Antiholomorphic correspondences and mating II: Shabat polynomial slices." Arxiv:2509.12357 https://arxiv.org/abs/2509.12357

talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.