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The Fully Inhomogeneous -Adic Littlewood Conjecture
Menny Aka, Alexander Gorodnik, Pankaj Vishe +1
We prove that for almost every $α\in\RR$, the \textit{fully inhomogeneous -adic Littlewood Conjecture} holds; namely, \begin{equation*} \forall δ\in\RR,\forall κ\in\ZZ_p, \;\;\l…
The Structure of Almost Stationary Measures
Ilya Gekhtman, Simon Machado, Omri Solan +1
Let be a higher-rank simple Lie group acting on a space . A theorem of Nevo and Zimmer asserts that every ergodic stationary probability measure on is either -invaria…
Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and Stück-Zimmer Theorem
Ilya Gekhtman, Simon Machado, Omri Solan +1
Fraczyk and Gelander proved in \cite{FG} that for any simple Lie group of high rank and for every non-lattice discrete subgroup , the injectivity radius of points in $…
Directional -Adic Littlewood Conjecture for Algebraic Vectors
Yuval Yifrach
For every vector $\overline α\in \RR^n$ and for every rational approximation $(\overline p,q)\in \RR^n\times\RR$ we can associate the displacement vector . We focus…
K-divergent lattices
Guy Lachman, Anurag Rao, Uri Shapira +1
We introduce a novel concept in topological dynamics, referred to as -divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogen…
Tori Approximation of Families of Diagonally Invariant Measures
Omri Nisan Solan, Yuval Yifrach
We approximate any portion of any orbit of the full diagonal group in the space of unimodular lattices in $\RR^n$ using a fixed proportion of a compact -orbit. Using those a…