Dynamics and universality of unimodal mappings with infinite criticality

Genadi Levin*, Grzegorz Światek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We consider infinitely renormalizable unimodal mappings with topological type which are periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point increases to infinity. It is shown that a limiting dynamics exists, with a critical point that is flat, but still having a well-behaved analytic continuation to a neighborhood of the real interval pinched at the critical point. We study the dynamics of limiting maps and prove their rigidity. In particular, the sequence of fixed points of renormalization for finite criticalities converges, uniformly on the real domain, to a mapping of the limiting type.

Original languageAmerican English
Pages (from-to)103-133
Number of pages31
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 2005


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