MATSUMOTO Keiji, OIKAWA Takashi,
Limits of iterations of complex maps and hypergeometric functions.
Hokkaido Mathematical Journal, 41 (2012) pp.135-155
We consider the limit of the iteration of a map z ↦ m(z) from a complex domain D to D. For two kinds of maps m, we show that each iteration mn(z) of m(z) converges for any z ∈ D as n → ∞ and that this limit is expressed by the hypergeometric function. These are analogs of the expression of the arithmetic-geometric mean by the Gauss hypergeometric function.
|Uncontrolled Keywords||limit of iteration, hypergeometric function|