Pooja Phogat

activity

20242026

collaborators

4 papers

math.DS2026

Chebyshev's method applied to polynomials with rotational symmetry

Tarakanta Nayak, Pooja Phogat

We investigate the dynamics of Chebyshev's method applied to the polynomial family $p_{n} (z) = z (z^{n} - 1)$ for $n > 1$ . The resulting map is denoted by $C_{n}$ . It is proved that the immedia…

math.DS2025

Chebyshev's method applied to polynomials with two distinct roots

Tarakanta Nayak, Pooja Phogat

The Julia set of the Chebyshev's method applied to polynomials with exactly two distinct roots is shown to be connected, and its Fatou set is proved to be the union of attracting b…

math.DS2025

Newton's method applied to rational functions: Fixed points and Julia sets

Tarakanta Nayak, Soumen Pal, Pooja Phogat

For a rational function $R$ , let $N_{R} (z) = z - \frac{R ( z )}{R ^{'} ( z )} .$ Any such $N_{R}$ is referred to as a Newton map. We determine all the rational functions $R$ for which $N_{R}$ has exact…

math.DS2024

Chebyshev's method for exponential maps

Subhasis Ghora, Tarakanta Nayak, Soumen Pal +1

It is proved that the Chebyshev's method applied to an entire function $f$ is a rational map if and only if $f (z) = p (z) e^{q (z)}$ , for some polynomials $p$ and $q$ . These are refe…