| Autor: |
Crovisier, Sylvain, Lyubich, Mikhail, Pujals, Enrique, Yang, Jonguk |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show that under renormalization, maps eventually become H\'enon-like, and then converge super-exponentially fast to the space of one-dimensional unimodal maps. We also completely characterize the local geometry of every stable and center manifolds that exist in these systems. The theory is based upon a quantitative reformulation of the Oseledets-Pesin theory yielding a unicritical structure of the maps in question comprising regular Pesin boxes co-existing with "critical tunnels" and "valuable crescents". In forthcoming notes we will show that infinitely renormalizable perturbative H\'enon-like maps of bounded type belong to our class. |
| Databáze: |
arXiv |
| Externí odkaz: |
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