Geodesic
Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map
S.S. Belmesova1 ; L.S. Efremova1 ; D. Fournier-Prunaret2
1 Lobachevsky Nizhny Novgorod State University (Research University), Nizhny Novgorod, Russia
2 LAAS-CNRS, INSA, University of Toulouse, France
ESAIM. Proceedings, Tome 46 (2014), pp. 98-110.

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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).
DOI : 10.1051/proc/201446009

S.S. Belmesova 1 ; L.S. Efremova 1 ; D. Fournier-Prunaret 2

1 Lobachevsky Nizhny Novgorod State University (Research University), Nizhny Novgorod, Russia
2 LAAS-CNRS, INSA, University of Toulouse, France 
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     title = {Invariant {Curves} of {Quadratic} {Maps} of the {Plane} from the {One-Parameter} {Family} {Containing} the {Trace} {Map}},
     journal = {ESAIM. Proceedings},
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S.S. Belmesova; L.S. Efremova; D. Fournier-Prunaret. Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map. ESAIM. Proceedings, Tome 46 (2014), pp. 98-110. doi : 10.1051/proc/201446009. http://geodesic.mathdoc.fr/articles/10.1051/proc/201446009/

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