Effective equidistribution for generalized higher step nilflows

• DOI: 10.48550/arxiv.2001.09789
• Publication Date: 2020-01-01
• Authors: Minsung Kim
• Keywords: Equidistributed sequence; Orbit (dynamics); Counterexample; Exponent; Diophantine approximation

The main results of this paper are to prove bounds for ergodic averages nilflows on general higher step nilmanifolds. Under Diophantine condition the frequency a toral projection flow, we that almost all orbits become equidistributed at polynomial speed. We analyze exponent with speed decay which is determined by number steps and structure nilpotent Lie algebras. result follows from technique over controlling scaling operators in irreducible representations measure estimation close return orbit