Difference between revisions of "Fatou coordinates"
Jump to navigation
Jump to search
(Created some stub) |
(minornaming correction) |
||
| Line 1: | Line 1: | ||
| − | Fatou coordinates - a term predominantly used in [[holomorphic dynamics]] - usually refers to one of the $2m$ [[principal Abel | + | Fatou coordinates - a term predominantly used in [[holomorphic dynamics]] - usually refers to one of the $2m$ [[principal Abel function]]s of a holomorphic function $f$ with [[parabolic fixpoint]] (which we assume for simplicity to be located at 0): |
$$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$ | $$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$ | ||
== Literature == | == Literature == | ||
* Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p. | * Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p. | ||
Revision as of 11:47, 5 June 2011
Fatou coordinates - a term predominantly used in holomorphic dynamics - usually refers to one of the $2m$ principal Abel functions of a holomorphic function $f$ with parabolic fixpoint (which we assume for simplicity to be located at 0): $$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$
Literature
- Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p.