| Title: | On the renormalization of systems with shearless tori |
| Author: | H. Koch |
| Abstract: | Renormalization has been successful in explaining universal scaling phenomena that accompany the breakup of invariant tori in the presence of shear. Similar phenomena have been observed numerically for invariant circles that are shearless, in the sense that their rotation number is locally minimal or maximal. This suggests that renormalization arguments should apply here as well. Our goal was to investigate this question by numerically implementing a renormalization transformation. This turned out to be more challenging than expected. We describe some partial result, problems that were encountered, and a new approach to the renormalization of Hamiltonians. Similar ideas may be useful in other renormalization-related problems. We are not assuming that the reader is familiar with the breakup of invariant tori or renormalization. Our main focus is on the notion of universality, and the necessary concepts will be introduced here. |
| Paper: | Preprint, program text, some data, and a README file. |
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