Some Results on Dynamics of Newton Differential Equation - Özer, Mehmet; Hacibekiroğlu, Gürsel; Valaristos, Antonis; Anagnostopoulos, Antonis N.; POLATOĞLU, YAŞAR (My University, 2005)
In this paper the case where the Newton differential equation defined by the Newton-Raphson iteration method equals a constant (namely 2) is investigated. The dynamics of these functions are examined by showing that the solution function can only be a Mbius transformation in the form of . The result obtained after the iterations carried out for the parameters a = 0.1 and b = 0.01 is the so-called Fibonacci sequences.
Keywords: dynamical system; Newton derivative; Mbius transformation; Fibonacci sequences