Structural stability of exponential functions described by orbit of zeroFootnote^∗

^∗Project supported by the National Natural Science Foundation of China.

References

• Baker , I.N. 1968 . Repulsive fixpoints of entire functions . Math. Z. , 104 : 252 – 256 .
   Web of Science ®Google Scholar
• Baker , I.N. and Rippon , P. J. 1984 . Iteration of exponential functions . Ann. Acad. Sci. Fenn. Ser. A. I. Math. , 9 : 49 – 77 .
   Google Scholar
• Devaney , R.L. 1984 . Julia sets and bifurcation diagrams for exponential maps . Bull Amer. Math. Sci. , 11 : 167 – 171 .
   Web of Science ®Google Scholar
• Devaney , R.L. , Goldberg , L.R. and Hubbard , J.H. 1985 . “ A dynamical approximation to the exponential map by polynomials ” . MSRI preprint
   Google Scholar
• Douady , A. and Hubbard , J.H. 1984,1985 . Étude dynamique des polynômcs complexes . Publ Math. d'Orsay, I , 2,4 II
   Google Scholar
• Eremenko , A.E. 1989 . “ On the iteration of entire functions ” . In Ergodic Theory and Dynamic Systems , Vol. 23 , Warsaw : Banach Center Publ. .
   Google Scholar
• Eremenko , A.E. and Lyubich , M.Yu. 1990 . “ Dynamical properties of some classes of entire functions ” . Vol. 4 , IMS SUNY at Stony Brook . preprint
   Google Scholar
• Fatou , P. 1926 . Sur I'itération des fonctions transcendantes entieres . Acta Math. , 47 : 337 – 370 .
   Google Scholar
• Lynbich , M.Yu. 1983 . Some typical properties of the dynamics of rational mappings . Uspekhi Mat. Nauk , 38 : 197 – 198 .
   Google Scholar
• Milnor , J. 1990 . “ Dynamics in one complex variable:Introductory lectures ” . Vol. 5 , IMS SUNY at Stony Brook . preprint
   Google Scholar
• Ma[nbar]é , R. , Sad , P. and Sullivan , D. 1983 . On the dynamics of rational maps . Ann. Sci. École Norm. Sup. , 16 : 193 – 217 .
   Web of Science ®Google Scholar
• Lei , T. 1990 . Similarity between the Mandelbrot set and Julia sets . Commun. Math. Phys. , 134 : 587 – 617 .
   Web of Science ®Google Scholar
• Zhuan , Y. 1992 . “ Structural instability of exponential functions ” . Northern Illinois Univ . preprint
   Google Scholar