Non-Hyperbolic Points of 2-D Discrete (DE) Homogeneous Polynomial Systems

dc.contributor.advisor	Faina Berezovskaya
dc.contributor.author	SAUD FAHAD MOHANA ALDOSARY
dc.date	2021
dc.date.accessioned	2022-06-01T10:31:39Z
dc.date.available	2022-06-01T10:31:39Z
dc.degree.department	Mathematics
dc.degree.grantor	Howard University
dc.description.abstract	Let 𝑂(0,0) be an isolated equilibrium point of the two-dimensional (2D) discrete system: ' 𝑥#$% = 𝑥# + ℎ𝑃&(𝑥#, 𝑦#) , 𝑦#$% = 𝑦# + ℎ𝑄&(𝑥, 𝑦) (1) where 𝑃&(𝑥, 𝑦),𝑄&(𝑥, 𝑦) are homogenous polynomials of order 𝑚 ≥ 1 𝑃&( 𝑥, 𝑦) =3𝑝&'(,( 𝑥# &'(𝑦# ( & (+, 𝑄&( 𝑥, 𝑦) =3𝑞&'(,( 𝑥# &'(𝑦# ( & (+, for some integer 𝑚 ≥ 1 and 𝑝&'(,( , 𝑞&'(,( ∈ ℝ, 𝑘 = 0,…,𝑚. Assume ℎ is a small positive constant, and, 𝑃(0,0) = 𝑄(0,0) = 0. We can consider (1) to be the Euler’s approximation of the ODE system
dc.identifier.uri	https://drepo.sdl.edu.sa/handle/20.500.14154/57326
dc.language.iso	en
dc.title	Non-Hyperbolic Points of 2-D Discrete (DE) Homogeneous Polynomial Systems
sdl.thesis.level	Doctoral
sdl.thesis.source	SACM - United States of America

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