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Bounds for attractors and the existence of homoclinic orbits in the lorenz system

✍ Scribed by G.A. Leonov

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
921 KB
Volume
65
Category
Article
ISSN
0021-8928

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✦ Synopsis

Frequency estimates are derived for the Lyapunov dimension of attractors of non-linear dynamical systems. A theorem on the localization of global attractors is proved for the Lorenz system. This theorem is applied to obtain upper bounds for the Lyapunov dimension of attractors and to prove the existence of homoclinic orbits in the Lorenz system.

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