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Record Nr. |
UNINA9910154745403321 |
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Autore |
McMullen Curtis T. |
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Titolo |
Complex Dynamics and Renormalization (AM-135), Volume 135 / / Curtis T. McMullen |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1995 |
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ISBN |
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Descrizione fisica |
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1 online resource (229 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 317 |
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Disciplina |
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Soggetti |
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Renormalization (Physics) |
Polynomials |
Dynamics |
Mathematical physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index |
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Sommario/riassunto |
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Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the |
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