| Description |
1 online resource (v, 118 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1288 |
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Memoirs of the American Mathematical Society ; no. 1288.
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| Contents |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Laminations -- 1.2. "Pinched disk" model of the Mandelbrot set -- 1.3. Previous work -- 1.4. Overview of the method -- 1.5. Main applications -- 1.6. Organization of the paper -- 1.7. Acknowledgments -- Chapter 2. Invariant laminations: general properties -- 2.1. Invariant geodesic laminations -- 2.2. Laminational equivalence relations -- 2.3. General properties of invariant geodesic laminations -- Chapter 3. Special types of invariant laminations -- 3.1. Invariant geodesic laminations with quadratically critical portraits |
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3.2. Some special types of invariant geodesic laminations -- 3.3. Accordions of invariant geodesic laminations -- 3.4. Smart criticality -- 3.5. Linked quadratically critical invariant geodesic laminations -- 3.6. Invariant geodesic laminations generated by laminational equivalence relations -- Chapter 4. Applications: Spaces of topological polynomials -- 4.1. The local structure of the space of all simple dendritic polynomials -- 4.2. Two-dimensional spaces of \si_{ }-invariant geodesic laminations -- Bibliography -- Index -- Back Cover |
| Summary |
The so-called ""pinched disk"" model of the Mandelbrot set is due to A. Douady, J.H. Hubbard and W.P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation that, loosely speaking, ""pinches"" the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated ML |
| Notes |
"May 2020, volume 265, number 1288 (fifth of 7 numbers)." |
| Bibliography |
Includes bibliographical references |
| Subject |
Geodesics (Mathematics)
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Polynomials.
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Invariant manifolds.
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Combinatorial analysis.
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Dynamics.
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Geodesia -- Matemáticas
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Análisis combinatorio
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Polinomios
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Dinámica
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Combinatorial analysis
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Dynamics
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Geodesics (Mathematics)
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Invariant manifolds
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Polynomials
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Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Complex dynamical systems [See also 30D05, 32H50] -- Combinatorics and topology.
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Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Complex dynamical systems [See also 30D05, 32H50] -- Polynomials; rational maps; entire and me.
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Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Complex dynamical systems [See also 30D05, 32H50] -- Small divisors, rotation domains and line.
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| Form |
Electronic book
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| Author |
Oversteegen, Lex G., author.
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Ptacek, Ross, author.
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Timorin, Vladlen, author.
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| LC no. |
2020023492 |
| ISBN |
9781470461447 |
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1470461447 |
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