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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.
Pages
Analysis Student Seminar Fall 2021
Analysis Student Seminar Fall 2021
About
About me
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Posts
Density of powers
Published:
Problem: Show that for almost every $x>1$ that {$x^k\mod 1$} is dense in $[0,1]$.
The Fatou-Sullivan Dictionary
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(A lot of this table/post was written quickly and needs reorganization/explanation/citations.)
Cantor Sets I: Some Topology
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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.
Almost Tilings of the Unit Square (Part 1?)
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Note: This post first appeared on a now defunct blog on January 19, 2019
Test Post
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This should be a heading
portfolio
Portfolio item number 1
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Short description of portfolio item number 1
Portfolio item number 2
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Short description of portfolio item number 2
publications
Antiholomorphic correspondences and mating I: realization theorems
Published in Arxiv, 2023
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. (2023). " Antiholomorphic correspondences and mating I: realization theorems." Arxiv https://arxiv.org/abs/2303.02459
talks
Talk 1 on Relevant Topic in Your Field
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This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
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This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
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.