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- W4285394513 abstract "Given a polynomial p, the degree of its Chebyshev’s method (C_p) is determined. If p is cubic, then the degree of (C_p) is found to be 4, 6 or 7 and we investigate the dynamics of (C_p) in these cases. If a cubic polynomial p is unicritical or non-generic, then it is proved that the Julia set of (C_p) is connected. The family of all rational maps arising as the Chebyshev’s method applied to a cubic polynomial which is non-unicritical and generic is parametrized by the multiplier of one of its extraneous fixed points. Denoting a member of this family with an extraneous fixed point with multiplier (lambda ) by (C_lambda ), we have shown that the Julia set of (C_lambda ) is connected whenever (lambda in [-1,1])." @default.
- W4285394513 created "2022-07-14" @default.
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- W4285394513 date "2022-07-13" @default.
- W4285394513 modified "2023-10-16" @default.
- W4285394513 title "The Julia sets of Chebyshev’s method with small degrees" @default.
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- W4285394513 doi "https://doi.org/10.1007/s11071-022-07648-4" @default.
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