Invariant Peano curves of expanding Thurston maps

• 成果类型: Article
• 署名作者: Meyer, Daniel
• 署名单位: Constructor University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0091-0
• 发表日期: 2013
• 页码: 95-171
• 关键词: kleinian-groups; SCALING LIMITS; julia sets

摘要

We consider Thurston maps, i.e., branched covering maps f:S (2) -> S (2) that are post-critically finite. In addition, we assume that f is expanding in a suitable sense. It is shown that each sufficiently high iterate F = f (n) of f is semi-conjugate to z (d) :S (1) -> S (1), where d = deg F. More precisely, for such an F we construct a Peano curve gamma:S (1) -> S (2) (onto), such that Fa similar to gamma(z) = gamma(z (d) ) (for all zaS (1)).