Let f and h be transcendental entire functions and let g be a continuous and open map of the complex plane into itself with g ○ f = h ○ g. We show that if f satisfies a certain condition, which holds, in particular, if f has no wandering domains, then g-1(J(h)) = J(f). Here J(·) denotes the Julia set of a function. We conclude that if f has no wandering domains, then h has no wandering domains. Further, we show that for given transcendental entire functions f and h, there are only countably many entire functions g such that g ○ f - h ○ g.
|Original language||English (US)|
|Number of pages||10|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - May 1999|
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