3 research outputs found
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
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)
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
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)