Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
By Alexander Leibman. Ergodic Theory and Dynamical Systems, 2004
209 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/188f051d781119d465b5a650b490338da096174b
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Ergodic averages of commuting transformations with distinct degree polynomial iterates (2009, background): “, T are equal, convergence was established after a long series of intermediate results; the papers [11–13, 18, 21, 23, 30, 34] dealt with the important case of linear polynomials, and using the machinery introduced in [23], convergence for arbitrary polynomials was finally obtained in [24] except fo”
- The Mobius function is strongly orthogonal to nilsequences (2008, background): “On the other hand, these two categories are certainly closely related (and are, in some sense, equivalent); see [10] for further discussion.”
- Multiple recurrence and nilsequences (2005, unknown): “We make use of the following property several times, which appears in [M] for connected groups and is proved in Leibman [ Lei2 ] in a similar way for the general case:”
- Infinite-step nilsystems, independence and complexity (2011, methodology): “For this, we require an extra definition and one lemma from [25].”
- Multiple ergodic averages for three polynomials and applications (2006, unknown): “Fundamental properties of nilsys-tems, related to our discussion, were studied in [2], [29], [28], [23], and [24].”
- Nilsequences and a structure theorem for topological dynamical systems (2009, unknown): “A point x ∈ X [ d ] can be decomposed as x = ( x (cid:9) , x (cid:9)(cid:9) ) with x (cid:9) , x (cid:9)(cid:9) ∈ X [ d − 1 ] , where x (cid:9) = (x (cid:4) 0 : (cid:4) ∈ { 0 , } d − 1 ) and x (cid:9)(cid:9) = (x (cid:4) 1 : (cid:4) ∈ { 0 , 1 } d − 1 ) .”
- A non-conventional ergodic theorem for a nilsystem (2002, methodology): “The proof is a combination of the proof of Lesigne with the work of Leibman [8] on polynomial sequences in groups.”
- Pointwise convergence of ergodic averages along cubes (2010, background): “The factor being an inverse limit of nilsystems, one uses Leibman’s result [ 14 ] to give the pointwise convergence for nilsystems and extend it by approximation to the factor Zk−1.”
- Multiple recurrence and convergence for hardy sequences of polynomial growth (2009, unknown): “In this case, one can show ([ 28 ]) that there exists a nilmanifold ˆ X = ˆ G/ˆ Ŵ, where ˆ”
- The Möbius function and distal flows (2013, methodology): “1 of [9] using the constructions with disconnnected nilmanifolds as in [15].”