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Bounds for attractors and the existence of homoclinic orbits in the lorenz system
Institution:1. Department of Mathematics, Federal University of Paraíba, 58051-900, João Pessoa-PB, Brazil;2. Department of Mathematics, Federal University of Pernambuco, 50740-540 Recife, PE, Brazil;1. Department of Mathematics and Statistics, University of Victoria, PO Box 3060 STN CSC, Victoria, BC, V8P 5C3, Canada;2. Pacific Institute for the Mathematical Sciences, University of British Columbia, 4176-2207 Main Mall, Vancouver, BC, V6T 1Z4, Canada;1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal;2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Abstract: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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