Tarakanta Nayak

activity

20242026

collaborators

8 papers

math.DS2026

A Survey of Baker Wandering Domains

Sukanta Das, Tarakanta Nayak

Let $f : C \to C = C \cup {\infty}$ be a transcendental meromorphic function (possibly without any pole) with a single essential singularity, and that…

math.DS2026

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.CV2025

Herman Rings: Structure, Dynamics, and Open Problems

Gorachand Chakraborty, Subhasis Ghora, Tarakanta Nayak

The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoverie…

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.CO2025

Connectedness of independence attractors of graphs with independence number three

Moumita Manna, Tarakanta Nayak

An independent set in a simple graph $G$ is a set of pairwise non-adjacent vertices in $G$ . The independence polynomial of $G$ , denoted by $I_{G}$ is defined as $1 + a_1 z + a_2 z^2+…

math.CO2025

Circles and line segments as independence attractors of graphs

Garima Khetawat, Moumita Manna, Tarakanta Nayak

By an independent set in a simple graph $G$ , we mean a set of pairwise non-adjacent vertices in $G$ . The independence polynomial of $G$ is defined as $I_G(z)=a_0 + a_1 z + a_2 z^2+…