Bifurcation analysis of one-dimensional maps using the renormalization technique in a parameter space
✍ Scribed by Ikuo Matsuba
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 335 KB
- Volume
- 81
- Category
- Article
- ISSN
- 1042-0967
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✦ Synopsis
This paper derives a renormalization formula defined on the parameter space where mapping behavior is preserved, together with the equivalent potential function. In contrast to the universal function given by Feigenbaum, the behavior near the critical point is governed by the potential function. There are several interesting features which are shared by Feigenbaums universal function, such as the representation of the critical point in terms of the unstable fixed point of the potential function, but the mapping differs from the scaling. The one-dimensional mapping is considered as an example, and the critical point and the scaling, which are major constants characterizing chaos from the potential function, are calculated precisely.