Электронный каталог

Статья

Kadrov, V.
On Calculating the Dimension of Invariant Sets of Dynamicsystems / V.Kadrov, M.D.Malykh. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2025. – Vol. 33, No. 4. – P. 404-410. – URL: https://doi.org/10.22363/2658-4670-2025-33-4-404-410. – Bibliogr.: 20.

This work investigates numerical approaches for estimating the dimension of invariant sets ontowhich the trajectories of dynamic systems “wind”, with a focus on fractal and correlation dimensions. Whilethe classical fractal dimension becomes computationally challenging in spaces of dimension greater thantwo, the correlation dimension offers a more efficient and scalable alternative. We develop and implementa computational method for evaluating the correlation dimension of large discrete point sets generated bynumerical integration of differential equations. An analogy is noted between this approach and the Richardson–Kalitkin method for estimating the error of a numerical method. The method is tested on two representativesystems: a conservative system whose orbit lies on a two-dimensional torus, and the Lorenz system, a canonicalexample of a chaotic flow with a non-integer attractor dimension. In both cases, the estimated correlationdimensions agree with theoretical predictions and previously reported results. The developed software providesan effective tool for analysing invariant manifolds of dynamical systems and is suitable for further studies,including those involving reversible difference schemes and high-dimensional systems



Спец.(статьи,препринты) = С 17 а - Численный анализ. Исчисление конечных разностей. Интерполирование
ОИЯИ = ОИЯИ (JINR)2025