Orbits in Teichmüller dynamics admits a critical exponent gap

2024/11/14 by Omri N. Solan, Solan, Omri Nisan
Physics and Astronomy · #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2411.09144

Abstract

McMullen '03 constructs a collection of orbits SL₂(ℝ).x in H(1,1) with infinitely generated stabilizers stab_SL2(ℝ)(x). We prove a gap in the set of critical exponents of stabilizers of SL₂(ℝ)-orbits in H_g: for every x∈ H_g, either stab_SL2(ℝ)(x) is a lattice, or we have a uniform bound on the critical exponent δ(stab_SL2(ℝ)(x)) ≤ 1-ε_g.

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