Fractal basin boundaries in higher-dimensional chaotic scattering

✍ Scribed by David Sweet; Edward Ott

• Book ID: 104338060
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 93 KB
• Volume: 266
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00900-7

✦ Synopsis

We analyze a hard-walled billiard chaotic scattering system in three spatial dimensions. Our analysis of this system tests Ž a conjectured formula for the fractal dimension of 'typical' non-attracting chaotic sets in higher-dimensional systems e.g., . time-independent, Hamiltonian systems with more than two degrees of freedom . It also shows the occurrence, in a chaotic scattering system, of a fractal basin boundary whose structure is that of a continuous, nowhere differentiable surface. A ray optical experimental realization of the billiard is suggested, and would offer the possibility of a physical realization of this basic type of basin boundary structure.