HOME  >> ߥʡ

## ߥʡ

 ȯɽ Ѹ 2009ǯ0306 1400ʬ λ 2009ǯ0306 1800ʬ ž 6609漼 ߥʡ̾ ϳطϥߥʡ ȥ Complex quadratic rational maps and Puiseux series dynamics ʬ ¾ ֱ̾ Jan Kiwi ֱԽ° Pontificia Universidad Catlica de Chile The moduli space of complex quadratic rational maps (as dynamical systems) is isomorphic to $C^2$. We will show that the structure of moduli space near infinity may be studied with the aid of non-Archimedean dynamics. More precisely, we consider the non-Archimedean field L obtained as the completion of an algebraic closure (Puiseux series) of the field of formal Laurent series in one variable. We study iterations of quadratic rational maps with coefficients in L over the corresponding projective line. We obtain a complete description of the dynamical space and of the parameter space of these maps. We are able to use this description to obtain some results which are the natural analogue for complex quadratic rational maps of part of Branner and Hubbard's picture of the parameter space of complex cubic polynomials near infinity. In particular, we will show that objects such as solenoids and Mandelbrot tori parametrize dynamically relevant subsets of the moduli space of complex quadratic rational maps near infinity. ׻ϳطϥߥʡ https://www.math.kyoto-u.ac.jp/dynamics/