An inequality for laminations, Julia sets and ‘growing trees’
An inequality for laminations, Julia sets and ‘growing trees’
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DOI：
10.1017/s0143385702000032
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发表时间：
2002-01
影响因子：
0.9
通讯作者：
A. Blokh;G. Levin
中科院分区：
文献类型：
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作者：
A. Blokh;G. Levin
For a closed lamination on the unit circle invariant under z\mapsto z^d we prove an inequality relating the number of points in the ‘gaps’ with infinite pairwise disjoint orbits to the degree; in particular, this gives estimates on the cardinality of any such ‘gap’ as well as on the number of distinct grand orbits of such ‘gaps’. As a tool, we introduce and study a dynamically defined growing tree in the quotient space. We also use our techniques to obtain for laminations an analog of Sullivan's no wandering domain theorem. Then we apply these results to Julia sets of polynomials.
