O. Solan

collaborators

7 papers

math.DS2026

The Structure of Almost Stationary Measures

Ilya Gekhtman, Simon Machado, Omri Solan +1

Let $G$ be a higher-rank simple Lie group acting on a space $X$ . A theorem of Nevo and Zimmer asserts that every ergodic stationary probability measure on $X$ is either $G$ -invaria…

math.DS2026

Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and StÃ¼ck-Zimmer Theorem

Ilya Gekhtman, Simon Machado, Omri Solan +1

Fraczyk and Gelander proved in \cite{FG} that for any simple Lie group $G$ of high rank and for every non-lattice discrete subgroup $I^ \leq G$ , the injectivity radius of points in…

math.DS2025

Geometric interpretation of quantitative instability

Omri N. Solan, Nattalie Tamam

Given a real algebraic group $G$ acting on a linear space $V$ , a vector $v \in V$ is called unstable if $0 \in G v - G v$ , where the closure is taken with respect to the Zaris…

math.DS2025

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 $A$ in the space of unimodular lattices in $\RR^n$ using a fixed proportion of a compact $A$ -orbit. Using those a…

math.DS2024

Birkhoff generic points on curves in horospheres

Omri Nisan Solan, Andreas Wieser

Let ${a_{t} : t \in R} < S L_{d} (R)$ be a diagonalizable subgroup whose expanding horospherical subgroup $U < S L_{d} (R)$ is abelian. By the Birkhoff ergodic…

math.DS2024

Orbits in TeichmÃ¼ller dynamics admits a critical exponent gap

Omri Nisan Solan

McMullen '03 constructs a collection of orbits $SL_{2} (R) . x$ in $H (1, 1)$ with infinitely generated stabilizers $\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(…