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Lyapunov dimension formula of attractors in the Tigan and Yang systems
G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova +1
In latter days the technique of attractors dimension estimate of Lorenz type systems is actively developed. In this work the Lyapunov dimension of attractors of the Tigan and Yang…
A short survey on Lyapunov dimension for finite dimensional dynamical systems in Euclidean space
G. A. Leonov, N. V. Kuznetsov
Nowadays there are a number of surveys and theoretical works devoted to the Lyapunov exponents and Lyapunov dimension, however most of them are devoted to infinite dimensional syst…
The Lyapunov dimension and its computation for self-excited and hidden attractors in the Glukhovsky-Dolzhansky fluid convection model
N. V. Kuznetsov, G. A. Leonov, T. N. Mokaev
Consideration of various hydrodynamic phenomena involves the study of the Navier-Stokes (N-S) equations, what is hard enough for analytical and numerical investigations since alrea…
The Lyapunov dimension formula for the global attractor of the Lorenz system
G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova +1
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting class…
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
N. V. Kuznetsov, G. A. Leonov, T. N. Mokaev +2
The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a {hidden attractor} in the…