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 exist
✦ LIBER ✦
The Existence of Shilnikov Homoclinic Orbits in the Michelson System: A Computer Assisted Proof
✍ Scribed by Daniel Wilczak
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 754 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1615-3375
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## Abstract We consider the Hamiltonian system in IR^__N__^ given by where __V__ : IR^__N__^ rarr; IR is a smooth potential having a non degenerate local maximum at 0 and we assume that there is an open bounded neighborhood ft of 0 such that V(__x__) < __V__(0) for __x__ δ Ω / {0}, __V(x)__ = __V
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