Homoclinic Points and Homoclinic Orbits for the Quadratic Family of Real Functions with Two Parameters - Open Access Library Journal

OALibJ > Vol.7 No.4, April 2020

Open Access Library Journal

Volume 7, Issue 4 (April 2020)

ISSN Print: 2333-9705 ISSN Online: 2333-9721

Google-based Impact Factor: 1.18 Citations

Homoclinic Points and Homoclinic Orbits for the Quadratic Family of Real Functions with Two Parameters ()

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DOI: 10.4236/oalib.1106170 374 Downloads 994 Views Citations

Author(s)

Karam N. Abdul-Kareem, Salma M. Farris

Affiliation(s)

Department of Mathematics, College of Computer and Mathematical Sciences, University of Mosul, Mosul, Iraq.

ABSTRACT

In this work, we study the homoclinic points and homoclinic orbits of the family of real functions with two parameters

. We show that the function

has no homoclinic points for

, but has a homoclinic point for

. Also, we prove that

has homoclinic orbits for

KEYWORDS

Local Unstable Set, Unstable Set, Homoclinic Point, Homoclinic Orbit

Share and Cite:

Abdul-Kareem, K. and Farris, S. (2020) Homoclinic Points and Homoclinic Orbits for the Quadratic Family of Real Functions with Two Parameters. Open Access Library Journal, 7, 1-18. doi: 10.4236/oalib.1106170.

Cited by

[1]	Homoclinic Bifurcation of a Quadratic Family of Real Functions with Two Parameters
	2021

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