Dynamics of a family of orbitally continuous mappings

Abhijit Pant; R. P. Pant; Kuldeep Prakash

doi:10.2298/FIL1711507P

Dynamics of a family of orbitally continuous mappings

Abhijit Pant, R. P. Pant, Kuldeep Prakash

Kumaun University India

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	3507-3517
Number of pages	11
Journal	Filomat
Volume	31
Issue number	11
DOIs	https://doi.org/10.2298/FIL1711507P
Publication status	Published - 2017
Externally published	Yes

Keywords

Bifurcation
Chaos
Forward asymptotic
Julia set
Multiple-lowering mapping
Periodic points

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1711507P

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AB - 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.

KW - Bifurcation

KW - Chaos

KW - Forward asymptotic

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KW - Multiple-lowering mapping

KW - Periodic points

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Dynamics of a family of orbitally continuous mappings

Abstract

Keywords

ASJC Scopus subject areas

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