Effective equidistribution for generalized higher-step nilflows

In this paper we prove bounds for ergodic averages for nilflows on general higher-step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at polynomial speed. We analyze the rate of decay which is deter...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2022-12, Vol.42 (12), p.3656-3715
Main Author: KIM, MINSUNG
Format: Article
Language:English
Subjects:
Algebra
Decay rate
Generators
Lie groups
Orbits
Original Article
Polynomials
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Summary:In this paper we prove bounds for ergodic averages for nilflows on general higher-step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at polynomial speed. We analyze the rate of decay which is determined by the number of steps and structure of general nilpotent Lie algebras. Our main result follows from the technique of controlling scaling operators in irreducible representations and measure estimation on close return orbits on general nilmanifolds.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.110