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| DC Field | Value | Language |
|---|
| contributor.author | Guru Prem Prasad, M | - |
| contributor.author | Nayak, T | - |
| date.accessioned | 2008-03-21T09:35:22Z | - |
| date.available | 2008-03-21T09:35:22Z | - |
| date.issued | 2007 | - |
| identifier.citation | Discrete and Continuous Dynamical Systems - Series A (DCDS-A), Vol 19, No 1, P 121- 138 | en |
| identifier.uri | http://aimsciences.org/journals/pdfs.jsp?paperID=2657&mode=abstract | - |
| identifier.uri | http://hdl.handle.net/2080/651 | - |
| description | Copyright for this article belongs to American Institute of Mathematical Sciences | en |
| description.abstract | In this paper, the dynamics of transcendental meromorphic functions
in the one-parameter family
M= {fλ(z) = λ f(z) : f(z) = tanh(ez) for z ∈ C and λ ∈ R \ {0} }
is studied. We prove that there exists a parameter value λ∗ ≈ −3.2946 such
that the Fatou set of fλ(z) is a basin of attraction of a real fixed point for
λ > λ∗ and, is a parabolic basin corresponding to a real fixed point for λ = λ∗.
It is a basin of attraction or a parabolic basin corresponding to a real periodic
point of prime period 2 for λ < λ∗. If λ > λ∗, it is proved that the Fatou
set of fλ is connected and, is infinitely connected. Consequently, the singleton
components are dense in the Julia set of fλ for λ > λ∗. If λ ≤ λ∗, it is proved
that the Fatou set of fλ contains infinitely many pre-periodic components and
each component of the Fatou set of fλ is simply connected. Finally, it is proved
that the Lebesgue measure of the Julia set of fλ for λ ∈ R \ {0} is zero. | en |
| format.extent | 759538 bytes | - |
| format.mimetype | application/pdf | - |
| language.iso | en | - |
| publisher | American Institute of Mathematical Sciences | en |
| subject | Fatou Sets | en |
| subject | Julia Sets | en |
| subject | Complex Dynamics | en |
| title | DYNAMICS OF {λ tanh(ez) : λ ∈ R \ {0}} | en |
| type | Article | en |
| Appears in Collections: | Journal Articles
|
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| tkanta-aims.pdf | | 741Kb | Adobe PDF | View/Open |
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