Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus
Giovanni Forni, William Goldman, Sean Lawton, Carlos Matheus
TL;DR
This paper demonstrates non-ergodic behavior in specific levels of SU(2) and SU(3) character varieties of the once-punctured torus using KAM theory, revealing complex dynamical structures.
Contribution
It introduces the application of KAM theory to identify non-ergodic levels in character varieties of the once-punctured torus, a novel approach in this context.
Findings
Existence of non-ergodic levels in SU(2) and SU(3) character varieties
Application of KAM theory to character variety dynamics
Identification of specific non-ergodic actions of hyperbolic elements
Abstract
Utilizing KAM theory, we show that there are certain levels in relative SU(2) and SU(3) character varieties of the once-punctured torus where the action of a single hyperbolic element is not ergodic.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals