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

Publisher： Edp Sciences

E-ISSN： 2267-3059|46|issue|98-110

ISSN： 2267-3059

Source： ESAIM: Proceedings and surveys, Vol.46, Iss.issue, 2014-12, pp. : 98-110

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Abstract

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).

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