Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906-1942American Mathematical Soc., 2012 - 454 pàgines The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others. |
Continguts
| 3 | |
1 | 10 |
Dynamics of a Complex History | 23 |
Iteration and Differential Equations | 33 |
3 | 39 |
Iteration and Differential Equations | 67 |
The United States | 95 |
5 | 103 |
Fatou and Julia in the 1920s | 213 |
The German Wave | 229 |
Siegel the Center Problem and KAM Theory | 253 |
Iteratin Around the Globe | 267 |
Appendix A Report on the Grand Prix des Sciences Mathématiques | 281 |
Singular Lines of Analytic Functions | 291 |
Appendix E Curves of Julia | 297 |
Appendix G The DenjoyWolff Theorem | 303 |
The Road to | 113 |
11 | 117 |
Works Written for the Grand Prix | 131 |
20 | 141 |
29 | 150 |
33 | 158 |
41 | 164 |
49 | 172 |
Iteration in Italy | 181 |
The Giants Fall | 197 |
58 | 207 |
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Académie algebraic analytic functions attracting fixed point Böttcher center problem Chapter coefficients complex dynamics complex functions component convergence Cremer curves defined Diophantine disc discussed entire functions example existence Fatou and Julia Fatou set function f functional equations fundamental circle holomorphic infinitely infinity invariant inverse investigation irrationally neutral fixed iteration of complex iteration of functions iteration of rational iterative family Julia set Kœnigs Latt`es Lemma limit functions linear mathematicians mathematics meromorphic functions modulus monograph Montel’s multiplier neighborhood neutral fixed points Newton’s method normal families paper periodic points perturbation Pfeiffer Picard Pincherle Pincherle’s plane polynomial preimages proof properties rational functions rational maps referred repelling points Riemann Ritt root of unity rotation satisfying Schröder equation Schröder functional Section sequence showed Siegel singular domains small divisors problem solution sommets study of iteration superattracting Theorem values variables wandering domains zero