The Julia sets of Chebyshev’s method with small degrees

Given a polynomial p, the degree of its Chebyshev’s method \(C_p\) is determined. If p cubic, then found to be 4, 6 or 7 and we investigate dynamics in these cases. cubic unicritical non-generic, it proved that Julia set connected. The family all rational maps arising as applied which non-unicritical generic parametrized by multiplier one extraneous fixed points. Denoting member this with an point \(\lambda \) \(C_\lambda \), have shown connected whenever \in [-1,1]\).