Rigidity in Dynamics

Rigidity in Holomorphic and Quasiregular Dynamics

We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.

Rigidity and Inflexibility in Conformal Dynamics

Rigidity of C∗-algebras associated to dynamics

Dynamics of Quadratic Polynomials. Ii. Rigidity.

This is a continuation of the series of notes on the dynamics of quadratic polynomials. The first part of this series [L3] will be systematically used for the reference. In particular we will assume that the reader is familiar with the background outlined in §2 of Part I: quadratic-like maps, straightening, combinatorial classes, external rays, the Mandelbrot set M , secondary limbs, puzzle, et...

Nonlinearity, Quasisymmetry, Differentiability, And Rigidity in One-Dimensional Dynamics

In this article, we review some of our research in the study of one-dimensional dynamical systems, in particular, some technique and results in the study of the smooth classification of certain one-dimensional maps. The main results which we review are that if the conjugacy between two mixing and nice quasihyperbolic maps is differentiable at one point with uniform bound, then it is piecewise s...