I. Assani

activity

20032024

most citedA good universal weight for nonconventional ergodic averages in norm

7 citations · 40 across the 21 of their papers we have counts for

collaborators

23 papers

math.DS2024

Higher Order Wiener-Wintner systems: examples and applications

Idris Assani, Jacob Folks, Ryo Moore

We will construct ``higher-dimensional" versions of the Wiener-Wintner dynamical system that was originally studied by I. Assani in 2003. We will show that on these systems we can…

math.DS2022

Syracuse Maps as Non-singular Power-Bounded Transformations and Their Inverse Maps

Idris Assani, Ethan Ebbighausen, Anand Hande

We prove that the dynamical system $(N, 2^{N}, T, μ)$ , where $μ$ is a finite measure equivalent to the counting measure, is power-bounded in $L^{1} (μ)$ if and only…

math.DS2022

Collatz map as a non-singular transformation

Idris Assani

Let $T$ be the map defined on $N = {1, 2, 3, ...}$ by $T (n) = \frac{n}{2}$ if $n$ is even and by $T (n) = \frac{3 n + 1}{2}$ if $n$ is odd. Consider the dynamical system $(\N, 2^{\N},…

math.DS2021

Non-Autonomous Spatial-Temporal Differentiation Theorems for Group Endomorphisms

Idris Assani, Aidan Young

We introduce a non-autonomous generalization of spatial-temporal differentiations, and prove results about probabilistically and topologically generic behaviors of certain spatial-…

math.DS2021

Spatial-Temporal Differentiation Theorems

Idris Assani, Aidan Young

Let $(X, B, μ, T)$ be a dynamical system where $X$ is a compact metric space with Borel $σ$ -algebra $B$ , and $μ$ is a probability measure that's ergodic with re…

math.DS2020

New Estimates on the bounds of Brunel's operator

I. Assani, R. S. Hallyburton, S. McMahon +2

We study the coefficients of the Taylor series expansion of powers of the function $ψ (x) = \frac{1 - 1 - x}{x}$ , where the Brunel operator $A \equiv A (T)$ is defined as $ψ (T)$ for…