Renormalization and 3-manifolds which fiber over the circle
著者
書誌事項
Renormalization and 3-manifolds which fiber over the circle
（Annals of mathematics studies, no. 142）
Princeton University Press, 1996
- : cl : alk. paper
- : pbk : alk. paper
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: cl. : alk. paper410//A 5//1-142119713757,
: pbk. : alk. paper410//A 5//1-142119606549 -
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注記
Includes bibliographical references (p. 241-249) and index
内容説明・目次
- 巻冊次
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: pbk : alk. paper ISBN 9780691011530
内容説明
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
目次
1Introduction12Rigidity of hyperbolic manifolds113Three-manifolds which fiber over the circle414Quadratic maps and renormalization755Towers956Rigidity of towers1057Fixed points of renormalization1198Asymptotic structure in the Julia set1359Geometric limits in dynamics15110Conclusion175Appendix A. Quasiconformal maps and flows183Appendix B. Visual extension205Bibliography241Index251
- 巻冊次
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: cl : alk. paper ISBN 9780691011547
内容説明
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle.
Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
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