Exact Numerical Methods in Dynamical Systems Theory

✍ Scribed by Carsten Knudsen; Ole Stauning

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 606 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00067-8

✦ Synopsis

Interval mathematics is applied to computational problems in dynamical systems theory[ We present methods of global analysis that automatically verify the existence and uniqueness of all periodic orbits of _xed period of iterated mappings[ Furthermore\ the method is generalised to include parameter space in the global analysis[ A method is developed that computes a guaranteed enclosure of invariant sets of iterated mappings^the invariant sets may contain chaotic attractors or chaotic repellers[ The methods are applied to the logistic map\ the He non map and a two!dimensional trigonometric map[