Analytic pseudo-rotations

2022/10/07 by Berger, Pierre · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2210.03438

Abstract

We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen ergodic or to the contrary with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solve a problem of Herman (1998). One aspect of the proof provides a new approximation theorem, it enables in particular to implement the Anosov-Katok scheme in new analytic settings.

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• Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk
• On Kolmogorov-typical properties of symplectic dynamics

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