Symmetry Breaking and Fractal Dependence on Initial Conditions in Dynamical Systems: Ordinary Differential Equations of Thermal Convection
✍ Scribed by R. Rynio; A. Okniński
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 353 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0960-0779
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✦ Synopsis
A system of n 2 ordinary di}erential equations with discrete symmetry describing thermal convection in ~uids is investigated[ It is shown that the boundary structure of basins of co!existing\ non! symmetric attractors\ which are present after symmetry breaking\ is determined by stable manifolds of the symmetric repellers[ Moreover\ boundary components fall into two classes] separating boundaries\ dim"W S # n-0\ or non!separating boundaries\ dim"W S #³n-0\ where n is the dimension of the phase space[ Geometry of a basin boundary\ formed in the regular regime of dynamics is explained and shown to be quasi!fractal[