Yi-Chiuan Chen

activity

20182023

collaborators

4 papers

math.DS2023

From Hyperbolic to Parabolic Parameters along Internal Rays

Yi-Chiuan Chen, Tomoki Kawahira

For the quadratic family $f_{c} (z) = z^{2} + c$ with $c$ in a hyperbolic component of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. In this p…

math.DS2022

Holomorphic Shadowing for Hénon Maps Revisited: an Implicit Function Theorem Perspective

Yi-Chiuan Chen

In studying the complex Hénon maps, Mummert (in "Holomorphic shadowing for Hénon maps" Nonlinearity 21 pp. 2887-2898, 2008) defined an operator the fixed points of which give rise…

math.DS2018

Simple Proofs for the Derivative Estimates of the Holomorphic Motion near Two Boundary Points of the Mandelbrot Set

Yi-Chiuan Chen, Tomoki Kawahira

For the complex quadratic family $q_{c} : z \mapsto z^{2} + c$ , it is known that every point in the Julia set $J (q_{c})$ moves holomorphically on $c$ except at the boundary points of the Mand…

math.DS2018

From Cantor to Semi-hyperbolic Parameter along External Rays

Yi-Chiuan Chen, Tomoki Kawahira

For the quadratic family $f_{c} (z) = z^{2} + c$ with $c$ in the exterior of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. Let $c^$ be a…