Kuldeep Prakash - Academia.edu (original) (raw)

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Papers by Kuldeep Prakash

Research paper thumbnail of On the Dynamics of a Family of Rational Functions Which Contains Koebe Function

International Journal of Pure and Apllied Mathematics, 2016

We study the dynamics of a parameterized family of quadratic rational functions z → λz/(1 − z) 2 ... more We study the dynamics of a parameterized family of quadratic rational functions z → λz/(1 − z) 2 , λ ∈ (0, ∞). We have investigated the dynamical and geometric properties of Julia sets and the nature of the variance of these properties according to the parameter. We have shown the Julia sets are connected when λ 1 and are dynamically defined cantor sets when λ < 1. We also have shown the continuity of geometric properties specially in terms of Hausdorff dimensions of these Julia sets.

Research paper thumbnail of Dynamics of a family of orbitally continuous mappings

Filomat, 2017

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-line... more The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

Research paper thumbnail of On the Dynamics of a Family of Rational Functions Which Contains Koebe Function

International Journal of Pure and Apllied Mathematics, 2016

We study the dynamics of a parameterized family of quadratic rational functions z → λz/(1 − z) 2 ... more We study the dynamics of a parameterized family of quadratic rational functions z → λz/(1 − z) 2 , λ ∈ (0, ∞). We have investigated the dynamical and geometric properties of Julia sets and the nature of the variance of these properties according to the parameter. We have shown the Julia sets are connected when λ 1 and are dynamically defined cantor sets when λ < 1. We also have shown the continuity of geometric properties specially in terms of Hausdorff dimensions of these Julia sets.

Research paper thumbnail of Dynamics of a family of orbitally continuous mappings

Filomat, 2017

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-line... more The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

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