Host-Kra factors for $\bigoplus_{p \in P} \mathbb{Z} / p \mathbb{Z}$ actions and finite-dimensional nilpotent systems

Ergodic theorems, spectral theory, Markov operators (37A30) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) General groups of measure-preserving transformations and dynamical systems (37A15) Homogeneous flows (37A17) Relations between ergodic theory and number theory (37A44)

Cites Work

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Norm convergence of nilpotent ergodic averages
The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
An odd Furstenberg-Szemerédi theorem and quasi-affine systems
Multiple recurrence and convergence results associated to $\mathbb F_P^\omega$-actions
Extensions of ergodic group actions
Polynomial sequences in groups
Some aspects of dimension theory for topological groups
The logarithmic Sarnak conjecture for ergodic weights
Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
Strictly ergodic distal models and a new approach to the Host-Kra factors
The structure theory of nilspaces. I
The structure theory of nilspaces. III: Inverse limit representations and topological dynamics
The structure of compact groups. A primer for the student -- A handbook for the expert
An inverse theorem for the uniformity seminorms associated with the action of $\mathbb F_p^\infty$
Nonconventional ergodic averages and nilmanifolds
Transformation groups and $C^ *$-algebras
On some types of topological groups
Flows on Homogeneous Spaces. (AM-53)
Compact Lie Groups
Universal characteristic factors and Furstenberg averages
Automatic Continuity of Group Homomorphisms
Théorèmes ergodiques pour des mesures diagonales
Coboundaries and Homomorphisms for Non-Singular Actions and a Problem of H. Helson
On sets of integers containing k elements in arithmetic progression
Nilpotent Structures in Ergodic Theory
The structure theory of Nilspaces II: Representation as nilmanifolds
Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
On nilspace systems and their morphisms
Multiple recurrence and large intersections for abelian group actions
AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
Compact abelian group extensions of discrete dynamical systems
Dynamical Systems on Nilmanifolds
A non-conventional ergodic theorem for a nilsystem
Spaces With a Compact Lie Group of Transformations
Multiple ergodic averages in abelian groups and Khintchine type recurrence
An inverse theorem for the Gowers $U^{s+1}[N$-norm]
A new proof of Szemerédi's theorem
On higher-order Fourier analysis in characteristic p
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
Host–Kra theory for -systems and multiple recurrence

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Host-Kra factors for \(\bigoplus_{p \in P} \mathbb{Z} / p \mathbb{Z}\) actions and finite-dimensional nilpotent systems