Showing math.DSShow all
3 papers · 1 filter
math.DS2026
On the spectral analysis of dynamical Möbius-Sarnak process and topological entropy of Möbius fonction
el Houcein el Abdalaoui
By extending the Rokhlin-Sinai machinery relating to the entropy and countable Lebesgue component in the spectrum, we establish that the dynamical Möbius-Sarnak process has a coun…
math.DS2026
Operator ergodic theorems with Möbius "weights"
El Houcein El Abdalaoui, Michael Lin
Motivated by Sarnak's conjecture in topological dynamics for the Möbius function , we study, for a power-bounded on a Banach space , the weak convergence $$ (*) \qquad…
math.DS2025
On the homogeneous ergodic bilinear averages with -bounded multiplicative weights
el Houcein el Abdalaoui
We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic -bounded multiplicative function $\bo…