The Lyapunov dimension was named after the Russian mathematician Aleksandr Lyapunov because of the close connection with the Lyapunov exponents. Definitions · Definition via finite-time... |
| Lyapunov dimension |  |
В математике динамических систем понятие ляпуновской размерности было предложено Капланом и Йорком для оценки хаусдорфовой размерности аттракторов.
В дальнейшем концепция получила развитие и строгое обоснование в ряде работ, и в настоящее время... Википедия (Английский язык)
Leonov G.A., Seledzhi S.M., “Lyapunov Dimension of Attractors of the Lorenz-Like Differential Equations”, Proceedings of the 3rd International Conference on ... |
17 февр. 2016 г. · In this survey the invariance of Lyapunov dimension with respect to diffeomorphisms and its connection with the Leonov method are discussed. An ... |
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first ... |
2 июл. 2020 г. · An effective analytical method for the estimation of the Lyapunov dimension is presented, its application to self-excited and hidden attractors ... |
The fractal dimension of an attracting torus Tk in × Tk is shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. |
22 окт. 2024 г. · ... Physically, the Lyapunov exponents are the average exponential contraction/expansion rates in the N directions of the phase space along the ... |
The advantage of the method is that it allows one to estimate the Lyapunov dimension of invariant sets without localization of the set in the phase space and, ... |
In particular, J.L. Kaplan and J.A. Yorke defined a quantity they called Lyapunov dimension and conjectured that it was equal to information dimension. Kaplan ... |
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