Kodai Mathematical Journal
- Kodai Math. J.
- Volume 24, Number 1 (2001), 48-65.
On holomorphic families of rational maps: finiteness, rigidity and stability
We consider holomorphic families of rational maps from the viewpoint of complex dynamics.
First, we consider some classes of families of rational maps which satisfy a certain stability condition. We show a finiteness theorem for such holomorphic families of rational maps parameterized by a Riemann surface of finite type.
Next, we consider the monodromy of quasiconformally stable holomorphic families of rational maps over a punctured disk, and study the action of the monodromy on the Julia set.
Kodai Math. J., Volume 24, Number 1 (2001), 48-65.
First available in Project Euclid: 19 January 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 37F15: Expanding maps; hyperbolicity; structural stability
Shiga, Hiroshige. On holomorphic families of rational maps: finiteness, rigidity and stability. Kodai Math. J. 24 (2001), no. 1, 48--65. doi:10.2996/kmj/1106157295. https://projecteuclid.org/euclid.kmj/1106157295