Geodesic
On asymptotic values of functions in a polydisk domain and Bagemihl's theorem
Problemy analiza, Tome 4 (2015) no. 2, pp. 23-31

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Asymptotic sets of functions in a polydisk domain of arbitrary connectivity are studied. We construct an example of such function, having preassigned asymptotic set. This result generalizes well-known examples, obtained by M. Heins and W. Gross for entire functions. Moreover, it is found out that not all results on asymptotic sets of functions in $\mathbb{C}$ can be extended to functions in $\mathbb{C}^n$. In particular, this fact is connected with the failure of Bagemihl's theorem on ambiguous points for functions in $\mathbb{R}^n,$ $n\geq 3$.
Keywords: asymptotic value, analytic set, ambiguous point. 
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     author = {E. G. Ganenkova},
     title = {On asymptotic values of functions in a polydisk domain and {Bagemihl's} theorem},
     journal = {Problemy analiza},
     pages = {23--31},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2015_4_2_a2/}
}
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E. G. Ganenkova. On asymptotic values of functions in a polydisk domain and Bagemihl's theorem. Problemy analiza, Tome 4 (2015) no. 2, pp. 23-31. http://geodesic.mathdoc.fr/item/PA_2015_4_2_a2/