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Analytic proof of the emergence of new type of Lorenz-like attractors from the triple instability in systems with Z4-symmetry
Journal of Differential Equations. 2025. Vol. 430. Article 113189.
We study bifurcations of a symmetric equilibrium state in systems of differential equations invariant with respect to a Z4-symmetry. We prove that if the equilibrium state has a triple zero eigenvalue, then pseudohyperbolic attractors of different types can arise as a result of the bifurcation. The first type is the classical Lorenz attractor and the second type is the so-called Simó angel. The normal form of the considered bifurcation also serves as the normal form of the bifurcation of a periodic orbit with multipliers (-1,i,-i). Therefore, the results of this paper can also be used to prove the emergence of discrete pseudohyperbolic attractors as a result of this codimension-3 bifurcation, providing a theoretical confirmation for the numerically observed Lorenz-like attractors and Simó angels in the three-dimensional Hénon map
Keywords: Lorenz attractorаттрактор Лоренцагетероклинический контурpseudohyperbolic attractorsПСЕВДОГИПЕРБОЛИЧЕСКИЙ АТТРАКТОРheteroclinic connection
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