Squeezing functions and Cantor sets
| Autor: | Leandro Arosio, Nikolay Shcherbina, Erlend Fornaess Wold, John Erik Fornæss |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Mathematics - Complex Variables 010102 general mathematics Degenerate energy levels Mathematics::General Topology Function (mathematics) 01 natural sciences Julia set Unit disk Theoretical Computer Science Settore MAT/03 Mathematics (miscellaneous) Quadratic equation Hausdorff dimension 0103 physical sciences FOS: Mathematics Point (geometry) 010307 mathematical physics Complex Variables (math.CV) 0101 mathematics Mathematics |
| Popis: | We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point of view of the squeezing function. Finally we show that complements of Cantor sets arising as Julia sets of quadratic polynomials have degenerate squeezing functions, despite of having Hausdorff dimension arbitrarily close to two. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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