MathDB

Degree of polynomial recursion - OIMU 2005 Problem 1

Source:

September 3, 2010

algebrapolynomialanalytic geometrylimitinductionratioalgebra proposed

Problem Statement

Let

P(x,y)=(x^2y^3,x^3y^5)

P^1=P

and

P^{n+1}=P\circ P^n

. Also, let

p_n(x)

be the first coordinate of

P^n(x,x)

, and

f(n)

be the degree of

p_n(x)

. Find

\lim_{n\to\infty}f(n)^{1/n}