Abdul-Kareem, K.N. and Farris, S.M. (2020) Homoclinic Points and Bifurcation for a Quadratic Family with Two Parameters. MSc Thesis, Department of Mathematics, College of Computer and Mathematical Sciences, University of Mosul, Mosul, Iraq, 1-98.

has been cited by the following article:

• TITLE: Homoclinic Bifurcation of a Quadratic Family of Real Functions with Two Parameters

  AUTHORS: Salma M. Farris, Karam N. Abdul-Kareem

  KEYWORDS: Local Unstable Set, Unstable Set, Homoclinic Point, Homoclinic Orbit, Non-Degenerate, Homoclinic Tangency, Homoclinic Bifurcation

  JOURNAL NAME: Open Access Library Journal, Vol.8 No.5, May 31, 2021

  ABSTRACT: In this work the homoclinic bifurcation of the family H={h(a,b)(x)=ax2+b:a∈R/{0},b∈R} is studied. We proved that this family has a homoclinic tangency associated to x=0 of P1 for b=-2/a. Also we proved that Wu(P1) does not intersect the backward orbit of P1 for b>-2/a, but has intersection for b0. So H has this type of the bifurcation.