Gevrey regularity for the formally linearizable billiard of Treschev

2022/11/06 by Wang, Qun, Zhang, Ke
#37J40 #70H08 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.03182

Abstract

Treschev made the remarkable discovery that there exists formal power series describing a billiard with locally linearizable dynamics. We show that if the frequency for the linear dynamics is Diophanine, the Treschev example is (1+ α)-Gevrey for some α> 0. Our proof is based on an iterative scheme that further clarifies the structure and symmetries underlying the original Treschev construction. Hopefully, Our result sheds a light on the more important question of whether this example is convergent.

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