Geodesic
Certain dynamical aspects of a family f λ (z) = λ e z z+1 for z ∈ c when λ 0
Filomat, Tome 36 (2022) no. 2, p. 683

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We study the change of dynamics of transcendental meromorphic functions f λ = λ e z z+1 for z ∈ C when λ varies on the negative real axis. It is shown that there is a λ such that the Fatou set of f λ is empty for λ λ whereas the Fatou set is an invariant parabolic basin corresponding to a real rationally indifferent fixed point x if λ = λ. In fact, the Fatou set is an invariant attracting basin of a real negative fixed point a λ if λ λ 0. Also the dynamics of f n λ for n ≥ 2 at the fixed points is investigated for different values of λ. As a generalization of f λ , we observed some dynamical issues for the class of entire maps F λ,a,m (z) = λ(z + a) m exp(z) where λ, a ∈ C and m ∈ N
DOI : 10.2298/FIL2202683C
Classification : 37F10, 30D05, 37F50
Keywords: Bifurcation, meromorphic function, Fatou set, Julia set 
Gorac; and Chakraborty; Sanjib Kumar Datta; Debasmita Dutta. Certain dynamical aspects of a family f λ (z) = λ e z z+1 for z ∈ c when λ < 0. Filomat, Tome 36 (2022) no. 2, p. 683 . doi: 10.2298/FIL2202683C
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     title = {Certain dynamical aspects of a family f \ensuremath{\lambda} (z) = \ensuremath{\lambda} e z z+1 for z \ensuremath{\in} c when \ensuremath{\lambda} < 0},
     journal = {Filomat},
     pages = {683 },
     year = {2022},
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     doi = {10.2298/FIL2202683C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2202683C/}
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