A gallery of iterated correspondences.
A Proof of Simultaneous Linearization with a Polylog Estimate
We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schröder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.
Accessibility of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if A is completely invariant (i.e. ), and if μ is an arbitrary f-invariant measure with positive Lyapunov exponents on ∂A, then μ-almost every point q ∈ ∂A is accessible along a curve from A. In fact, we prove the accessibility of every “good” q, i.e. one for which “small neigh bourhoods arrive at large scale” under iteration of f. This generalizes the...
An algorithm for finding the Veech group of an origami.
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. (Summary).
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings.
Asymptotic behaviors of complex analytic dynamical systems.