Evolution Equations and Control Theory (EECT)

The $\varepsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors
Pages: 345 - 356, Issue 3, September 2017

doi:10.3934/eect.2017018      Abstract        References        Full text (360.3K)           Related Articles

María Anguiano - Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160, 41080-Sevilla, Spain (email)
Alain Haraux - CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France (email)

1 A. V. Babin and M. I. Vishik, Regular attractors of semigroups and evolution equations, J. Math. Pures Appl, 62 (1983), 441-491.       
2 Z. Chen, A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors, Chaos Solitons Fractals, 3 (1993), 575-582.       
3 V. V. Chepyzhov and A. A. Ilyin, A note on the fractal dimension of attractors of dissipative dynamical systems, Nonlinear Analysis, 44 (2001), 811-819.       
4 I. Dumer, M. S. Pinsker and V. V. Prelov, On coverings of ellipsoids in Euclidean spaces, Transactions on Information Theory, 50 (2004), 2348-2356.       
5 P. Li and S. T. Yau, On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys., 88 (1983), 309-318.       
6 R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, $2^{nd}$ edition, Springer-Verlag, New York, 1997.       
7 S. Zelik, The attractor for a nonlinear reaction-diffusion system with a supercritical nonlinearity and its dimension, Rend. Accad. Naz. Sci. XL Mem. Mem. Math. Appl., 24 (2000), 1-25.       

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