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math.DS2025
On the dynamics of Halley's method
Gang Liu, Soumen Pal, Saminathan Ponnusamy
In this article, we study the global dynamics of Halley's method applied to complex polynomials. Specifically, we analyze the structure and connectivity of the Julia set of this me…
math.DS2025
Newton's method applied to rational functions: Fixed points and Julia sets
Tarakanta Nayak, Soumen Pal, Pooja Phogat
For a rational function , let Any such is referred to as a Newton map. We determine all the rational functions for which has exact…