10 citations · 20 across the 6 of their papers we have counts for
7 papers
Conjugacy classes of real analytic one-dimensional maps are analytic connected manifolds
Trevor Clark, Sebastian van Strien
An important question is to describe topological conjugacy classes of dynamical systems. Here we show that within the space of real analytic one-dimensional maps with critical poin…
The dynamics of complex box mappings
Trevor Clark, Kostiantyn Drach, Oleg Kozlovski +1
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the retur…
Hyperbolicity of renormalization for dissipative gap mappings
Trevor Clark, Márcio Gouveia
A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which aris…
The boundary of chaos for interval mappings
Trevor Clark, Sofía Trejo
A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980's that the only route to positi…
Quasisymmetric rigidity in one-dimensional dynamics
Trevor Clark, Sebastian van Strien
In the late 1980's Sullivan initiated a programme to prove quasisymmetric rigidity in one-dimensional dynamics: interval or circle maps that are topologically conjugate are quasisy…
Dynamics of asymptotically holomorphic polynomial-like maps
Trevor Clark, Edson de Faria, Sebastian van Strien
The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of a…
Complex box bounds for real maps
Trevor Clark, Sebastian van Strien, Sofia Trejo
In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box…