About topological conjugacy of quadratic maps in unbounded domains
https://doi.org/10.26907/2949-3919.2025.4.4-18
Abstract
Pairwise topological conjugacy in some unbounded domains of the plane R2 of the quadratic map F(x, y) = xy, (x − 2)2 , the Lotka-Volterra map L(x, y) = (x(4 − x − y), xy) and the map H(x, y) = (y2, xy − 2x + 2), which arises in studying of the reflection and transmission coefficients of a plane wave with a given momentum in the field of a quasicrystalline lattice is proved in this paper. Using previous author’s results on the wandering points of the map F and the result of the paper we give a description of the set of wandering points of the maps L and H.
About the Authors
S. S. Belmesova
Lobachevskii Nizgny Novgorod State University
Russian Federation
Russian Federation
Svetlana Sergeevna Belmesova
23 Gagarin ave., Nizhny Novgorod 603022
L. S. Efremova
Lobachevskii Nizgny Novgorod State University; Moscow Institute of Physics and Technology
Russian Federation
Russian Federation
Lyudmila Sergeevna Efremova
23 Gagarin ave., Nizhny Novgorod 603022
9 Institutskii alley, Dolgoprudny, Moscow Region, 141701
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Review
For citations:
Belmesova S.S., Efremova L.S. About topological conjugacy of quadratic maps in unbounded domains. Mathematics and Theoretical Computer Science. 2025;3(4):4-18. (In Russ.) https://doi.org/10.26907/2949-3919.2025.4.4-18
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