M Kisaka 1995 Nonlinearity 8 273 doi:10.1088/0951-7715/8/2/009
Local uniform convergence and convergence of Julia sets
M Kisaka
Show affiliationsLet fn and f be entire functions and suppose that fn converges to f locally uniformly on C. Then if the Fatou set of f consists only of basins of attracting cycles or is empty, the Julia set of fn converges to that of f in the Hausdorff metric. We also show that expanding f implies the above assumption. Next we show that for each singular value c of f there exists a singular value c(n) of fn (for each sufficiently large n) converging to c. As an application, we propose a criterion which determines by the approximating sequence (fn)n=0infinity whether the Julia set of S is the whole sphere C for a certain class of entire functions.
- PACS
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05.45.-a Nonlinear dynamics and nonlinear dynamical systems
- MSC
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37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets
- Subjects
- Dates
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Issue 2 (March 1995)
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Local uniform convergence and convergence of Julia sets
M Kisaka 1995 Nonlinearity 8 273
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