12-38 K. Khanin, S. Kocic

Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks (673K, PDF) Apr 17, 12

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. We prove the renormalization conjecture for circle diffeomorphisms with breaks, i.e. that the renormalizations of any two $C^{2+lpha}$-smooth circle diffeomorphisms with a break point, with the same irrational rotation number and the same size of the break, approach each other exponentially fast in the $C^2$-topology. As a corollary, we obtain the following rigidity result: for almost all irrational rotation numbers, any two circle diffeomorphisms with a break, with the same rotation number and the same size of the break, are $C^1$-smoothly conjugate to each other.

Files: 12-38.src( 12-38.keywords , kocic_khanin_convergence_of_renormalizations.pdf.mm )