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Homeomorphisms of the mandelbrot Set / DeWitt Grothendieck.
Material type:
TextLanguage: English Series: phoenix MathematicsPublication details: India: Phoenix 2023.Edition: 1st edDescription: vi , 206 p .: ill . ; 23.5 cmSubject(s): DDC classification: - 516.375 GRO
Contents:
Summary: On subsets of the Mandelbrot set, EM ⊂ M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism h : EM → EM in the parameter plane. Each h has two fixed points in EM, and a countable family of mutually homeomorphic fundamental domains. Possible generalizations to other families of polynomials or rational mappings are discussed.
The homeomorphisms on subsets EM ⊂ M constructed by surgery are extended to homeomorphisms of M, and employed to study groups of non-trivial homeomorphisms h : M → M. It is shown that these groups have the cardinality of ℝ, and they are not compact.
1. on latt s maps 2. Branner hubbard motions and attracting dynamics 3.on cap[ture zones for the family .
| Item type | Current library | Collection | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 516.375 GRO (Browse shelf(Opens below)) | Available | 315667 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 516.375 GRO (Browse shelf(Opens below)) | Available | 315666 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 516.375 GRO (Browse shelf(Opens below)) | Available | 315665 |
1. on latt s maps 2. Branner hubbard motions and attracting dynamics 3.on cap[ture zones for the family .
On subsets of the Mandelbrot set, EM ⊂ M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism h : EM → EM in the parameter plane. Each h has two fixed points in EM, and a countable family of mutually homeomorphic fundamental domains. Possible generalizations to other families of polynomials or rational mappings are discussed.
The homeomorphisms on subsets EM ⊂ M constructed by surgery are extended to homeomorphisms of M, and employed to study groups of non-trivial homeomorphisms h : M → M. It is shown that these groups have the cardinality of ℝ, and they are not compact.