Phase Diagrams of Meromorphic Functions
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We describe the local normal forms of phase diagrams, study properties of their orbits, and investigate the basins of attraction of zeros. Special attention is paid to the interplay between zeros, poles and critical points. In particular we derive formulas which relate the numbers of these points in a Jordan domain G to the winding numbers of P f and V f along the boundary of G. A short proof of Walsh’s theorem on the critical points of Blaschke products serves as an illustration.
Keywordsmeromorphic function phase plot phase diagram basin of attraction visualization of complex functions Gauss-Lucas theorem Walsh theorem
2000 MSC30D30 30A99
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