Dynamics in one complex variable
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form...
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| Main Author: | |
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| Format: | eBook Book |
| Language: | English |
| Published: |
Princeton, N.J
Princeton University Press
2006
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| Edition: | 3rd ed. |
| Series: | Annals of mathematics studies |
| Subjects: | |
| ISBN: | 0691124884, 1400835534, 9780691124889, 9781400835539, 9780691124872, 0691124876 |
| Online Access: | Get full text |
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| Summary: | This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the Écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. |
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| Bibliography: | Includes bibliographical references (p. 277-291) and index |
| ISBN: | 0691124884 1400835534 9780691124889 9781400835539 9780691124872 0691124876 |