4 papers
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…