Poincaré recurrence and number theory: thirty years later
DOI10.1090/S0273-0979-2011-01343-XzbMath1417.37025OpenAlexW1989769190MaRDI QIDQ3094408
Publication date: 25 October 2011
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0273-0979-2011-01343-x
Ramsey theoryFurstenberg correspondence principlePoincaré recurrence theoremmultiple recurrence theorem
Ergodic theorems, spectral theory, Markov operators (37A30) Special sequences and polynomials (11B83) Ramsey theory (05D10) Combinatorial dynamics (types of periodic orbits) (37E15) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Relations between ergodic theory and number theory (37A44)
Related Items (4)
Cites Work
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- Multiple ergodic averages for flows and an application
- The Möbius function is strongly orthogonal to nilsequences
- Convergence of polynomial ergodic averages of several variables for some commuting transformations
- The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems
- Idempotent ultrafilters, multipleweak mixing and Szemerédi's theorem for generalized polynomials
- Multiple recurrence and convergence for Hardy sequences of polynomial growth
- Convergence of polynomial ergodic averages
- Nilsequences and a structure theorem for topological dynamical systems
- Linear equations in primes
- Uniformity seminorms on \(\ell^{\infty}\) and applications
- An ergodic Szemerédi theorem for IP-systems and combinatorial theory
- Topological dynamics and combinatorial number theory
- An ergodic Szemerédi theorem for commuting transformations
- Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
- Multiple recurrence theorem for measure preserving actions of a nilpotent group
- A nilpotent Roth theorem.
- Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
- Convergence of multiple ergodic averages along polynomials of several variables
- A density version of the Hales-Jewett theorem
- Set-polynomials and polynomial extension of the Hales-Jewett theorem
- The polynomial multidimensional Szemerédi theorem along shifted primes
- Elemental methods in ergodic Ramsey theory
- Pleasant extensions retaining algebraic structure. I
- Pleasant extensions retaining algebraic structure. II
- Nonconventional ergodic averages and nilmanifolds
- The primes contain arbitrarily long arithmetic progressions
- Norm convergence of continuous-time polynomial multiple ergodic averages
- From discrete- to continuous-time ergodic theorems
- Ergodic averages of commuting transformations with distinct degree polynomial iterates
- AN INVERSE THEOREM FOR THE GOWERSU4-NORM
- The Green-Tao Theorem on arithmetic progressions in the primes: an ergodic point of view
- Universal characteristic factors and Furstenberg averages
- Powers of sequences and recurrence
- Théorèmes ergodiques pour des mesures diagonales
- On sets of integers containing k elements in arithmetic progression
- On difference sets of sequences of integers. I
- Norm convergence of multiple ergodic averages for commuting transformations
- Multiple recurrence and convergence for sequences related to the prime numbers
- Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
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