Invariant Curves of Quadratic Maps of the Plane from the
One-Parameter Family Containing the Trace Map*

Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map*

The rigorous proofs are given: (1) for the existence of the unbounded invariant curves, containing the fixed point – source (μ + 1; 1), of the maps from the one-parameter family Fμ(x,y) = (xy, (x − μ)2), μ ∈ [0, 2]; (2) for the birth of the...

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Bibliographic Details
Main Authors:	Belmesova S.S., Efremova L.S., Fournier-Prunaret D.
Format:	Article
Language:	English
Published:	EDP Sciences 2014-11-01
Series:	ESAIM: Proceedings and Surveys
Subjects:	quadratic map fixed point invariant curve
Online Access:	http://dx.doi.org/10.1051/proc/201446009

Description
Summary:	The rigorous proofs are given: (1) for the existence of the unbounded invariant curves, containing the fixed point – source (μ + 1; 1), of the maps from the one-parameter family Fμ(x,y) = (xy, (x − μ)2), μ ∈ [0, 2]; (2) for the birth of the closed invariant curve from the elliptic fixed point (μ − 1; 1) for μ = 3 / 2. Numerical results are presented for the main steps of the evolution of this invariant curve, when μ changes in the interval (3 / 2, 2).
ISSN:	2267-3059