Rescaling limits of complex rational maps

We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space.It is shown that any given sequence of maps of degree $d \ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which are not postcritically finite. For quadratic rational maps, a complete description of the possible rescaling limits is given. These results are obtained employing tools from non-Archimedean dynamics

Interface of gender and culture

I greet you in the soothing waters of the Pacific. The birth waters of Hawai’i to the North, island of the dream time, and Aotearoa, to the south. Papua New Guinea to the West and Marquesas to the East. These islands are the gathering places of the world’s largest Continent, the Pacific. We of this continent know that her birth waters are our connection. We also know that she is woman identified. It is no surprise therefore that from Hawai’i to the north to Aotearoa in the south the positioning of women in each of these societies bears a different story to that of the women of the continent of Europe. This reality lived out in Hawai’i means women shared with men the ultimate leadership of peoples. This location of women power is named Kuhinanui. Many remarkable women of Hawai’i occupied this position. From times of peace throughout to the first clash with imposed new culture, women of Hawai’i led, bled, struggled, defied and kept the kukui of self belief burning. Genealogically Hawai’i is connected to her other sisters throughout the Pacific. The story of Kuhinanui Liliuokalani is poignant

Counting Hyperbolic Components

We give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles