Alexey Kazakov

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20202025

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math.DS2025

Cascades of Lorenz attractors in the Shimizu-Morioka model

Alexey Kazakov, Vladislav Koryakin, Klim Safonov +1

The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property pe…

math.DS2024

Analytic proof of the emergence of new type of Lorenz-like attractors from the triple instability in systems with $Z_{4}$ -symmetry

Efrosiniia Karatetskaia, Alexey Kazakov, Klim Safonov +1

We study bifurcations of a symmetric equilibrium state in systems of differential equations invariant with respect to a $Z_{4}$ -symmetry. We prove that if the equilibrium st…

math.DS2020

Scenarios for the Creation of Hyperchaotic Attractors of 3D Maps

Aikan Shykhmamedov, Efrosiniia Karatetskaia, Alexey Kazakov +1

We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have two positive Lyapunov ex…

Cascades of Lorenz attractors in the Shimizu-Morioka model

Analytic proof of the emergence of new type of Lorenz-like attractors from the triple instability in systems with Z4​-symmetry

Scenarios for the Creation of Hyperchaotic Attractors of 3D Maps

Analytic proof of the emergence of new type of Lorenz-like attractors from the triple instability in systems with $Z_{4}$ -symmetry