# Bishnu Hari SubediTribhuvan University · Central Department of Mathematics

Bishnu Hari Subedi

M.Phil. in Mathematics

## About

27

Publications

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35

Citations

Introduction

Bishnu Hari Subedi currently works at the Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal. Bishnu does research in Complex Dynamics. His current project is 'PhD Research Work'.

Additional affiliations

November 2011 - present

**Tribhuvan University, Kathmandu, Nepal**

Position

- Professor (Assistant)

Description

- PhD Fellow as well.

November 2008 - present

Education

November 2007 - October 2010

**Kathmandu University, Kavre, Nepal**

Field of study

- Mathematics

## Publications

Publications (27)

In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact topological holomorphic semigroups.

We prove that there exist three different transcendental entire functions that can have infinite number of domains which lie in the different periodic component of each of these functions and their compositions.

The subject of this paper is the well-known 3n + 1 problem of elementary number theory. This problem concerns with the behaviour of the iteration of a function which takes odd integers n to 3n + 1, and even integers n to n/2. There is a famous Collatz conjecture associated to this problem which asserts that, starting from any positive integer n, re...

We prove that there exist three entire transcendental functions that can have an infinite number of domains which lie in the pre-periodic component of the Fatou set each of these functions and their compositions.

In this poster presentation, we show under what conditions the Fatou, Julia, and escaping sets of a holomorphic semigroup are respectively equal to the Fatou, Julia and escaping sets of its proper subsemigroups.

We define commutator of a holomorphic semigroup, and on the basis of this concept, we define conjugate semigroups of a holomorphic semigroup. We prove that the conjugate semigroup is nearly abelian if and only if the given holomorphic semigroup is nearly abelian. We also prove that the image of each of Fatou, Julia, and escaping sets of a holomorph...

We investigate under what conditions the Fatou, Julia, and escaping sets of a transcendental semigroup are respectively equal to the Fatou, Julia, and escaping sets of their subsemigroups. We define the partial fundamental set and fundamental set of a holomorphic semigroup, and on the basis of these sets, we prove that the Fatou and escaping sets o...

In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact topological holomorphic semigroups and examples of compact topological holomorphic semigroups are the spaces of...

We prove that there exist three transcendental entire functions that can have infinite number of domains which lie in the wandering component of the Fatou set of each of these functions and their compositions. This result is a generalization of a result of [5].

We prove that there exist three transcendental entire functions that can have infinite number of domains which lie in the wandering component of the Fatou set of each of these functions and their compositions. This result is a generalization of a result of [5].

In complex dynamics, the complex plane is partitioned into invariant subsets. In classical sense, these subsets are of course Fatou set and Julia set. Rest of the abstract available with the full text

In this paper, we study fast escaping set of transcendental semigroup. We discuss some the structure and properties of fast escaping set of transcendental semigroup. We also see how far the classical theory of fast escaping set of transcendental entire function applies to general settings of transcendental semigroups and what new phenomena can occu...

We define commutator of a transcendental semigroup, and on the basis of this concept, we define conjugate semigroup. We prove that the conjugate semigroup is nearly abelian if and only if the given semigroup is nearly abelian. We also prove that image of each of escaping set, Julia set and Fatou set under commutator (affine complex conjugating maps...

We mainly generalize the notion of abelian transcendental semigroup to nearly abelian transcendental semigroup. We prove that Fatou set, Julia set and escaping set of nearly abelian transcendental semigroup are completely invariant. We investigate no wandering domain theorem in such a transcendental semigroup. We also obtain results on a complete g...

We investigate to what extent Fatou set, Julia set and escaping set of transcendental semigroup is respectively equal to the Fatou set, Julia set and escaping set of its subsemigroup. We define partial fundamental set and fundamental set of transcendental semigroup and on the basis of this set, we prove that Fatou set and escaping set of transcende...

For a non-trivial transcendental semigroup, escaping set I(S) is in general S-forward invariant and it is S-completely invariant if semigroup S is abelian. In the contrary of this result, we investigate completely invariant escaping set K(S) in different way even if semigroup S is not abelian and we discuss some properties and structure of such typ...

In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia set of transcendental semigroup and we see how far the results of classical transcendental dynamics generalized...

We prove that there exists a non-trivial transcendental semigroup S such that the wandering (or pre-periodic or periodic) components of Fatou set F(S) has at least a simply connected domain D.

In this paper, we mainly study hyperbolic semigroups from which we get non-empty escaping set and Eremenko's conjecture remains valid. We prove that if each generator of bounded type transcendental semigroup S is hyperbolic, then the semigroup is itself hyperbolic and all components of I(S) are unbounded

We prove that there exist three transcendental entire functions that have infinite number of domains which lie in the wandering component of each of these functions and their composites. This result is a generalization of the result of Dinesh Kumar, Gopal Datt and Sanjay Kumar. In particular, they proved that there exist two transcendental entire f...

In this paper, we prove that escaping set of transcendental semigroup is S-forward invariant. We also prove that if holomorphic semigroup is abelian, then Fatou set, Julia set and escaping set are S-completely invariant. We see certain cases and conditions that the holomorphic semigroup dynamics exhibits same dynamical behavior just like the classi...

In this paper, we prove that the escaping set of a transcendental semi group is S-forward invari-ant. We also prove that if a holomorphic semi group is a belian, then the Fatou, Julia, and escaping sets are S-completely invariant. We also investigate certain cases and conditions that the holomorphic semi group dynamics exhibits the similar dynamica...

For a transcendental entire function f, we study the structure and properties of the escaping set I(f) which consists of points whose iterates under f escape to infinity. We concentrate on Eremenko’s conjecture and we review some attempts of its proofs. A significant amount of progress in Eremenko’s conjecture has been made possible via fast escapi...

For a transcendental entire function f, the escaping set I (f) consists of points whose iterates tends to infinity under f and fast escaping set A(f) consists of points whose iterates tends to infinity as fast as possible. In this article, we examine the conditions that both sets have the structure of infinite spider's web.

Herbert Gunther Grassmann introduced the product of the form a ∧ b of two vectors a and b which is neither scalar nor a vector in ordinary sense. This product is known as exterior (outer) product and represents the plane segment determined by the vectors a and b. Sir Kingdom Clifford introduced geometric algebra by combining the usual dot (inner) p...

## Questions

Question (1)

Let A(

*f*) be a fast escaping set of transcendental entire function. For Lth level of A(*f*) is closed. How?