5 papers · 1 filter
Laminations and External Angles for Similarity Pairs
Danny Calegari, Alden Walker
A {\em similarity pair} is the dynamical system in generated by two maps and for . Associated to the dynamical system is an attrac…
Quasimorphisms and Pseudo-Anosov flows
Danny Calegari, Jonathan Zung
We describe two connections between the theory of quasimorphisms and pseudo-Anosov flows without perfect fits on closed hyperbolic 3-manifolds. First we show that for every such fl…
Big mapping class groups and rigidity of the simple circle
Danny Calegari, Lvzhou Chen
Let denote the mapping class group of the plane minus a Cantor set. We show that every action of on the circle is either trivial or semi-conjugate to a unique minimal act…
Surgery sequences and self-similarity of the Mandelbrot set
Danny Calegari
We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically…
Combinatorics of the Tautological Lamination
Danny Calegari
The Tautological Lamination arises in holomorphic dynamics as a combinatorial model for the geometry of 1-dimensional slices of the Shift Locus. In each degree the tautological…