Abstract
In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.
Original language | English (US) |
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Pages (from-to) | 27-47 |
Number of pages | 21 |
Journal | Journal of Statistical Physics |
Volume | 23 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1980 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Keywords
- Poincaré mapping
- attractor
- closed orbit
- linear system of equations in variations