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It is easy to see that no n-REA set can form a (non-trivial) min-imal pair with 00 and only slightly more dicult to observe that no !-REA set can form a (non-trivial) minimal pair with 000.
Entire functions for which the escaping set is a spider's web
Entire functions escaping set spider's web
2011/1/19
We construct several new classes of transcendental entire func-tions, f, such that both the escaping set, I(f), and the fast escaping set,A(f), have a structure known as a spider’s web. We show that s...
We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.