Bers and H\'enon, Painlev\'e and Schroedinger
Serge Cantat (IRMAR)

TL;DR
This paper explores the dynamics of mapping class groups on character varieties, revealing similarities with Hénon mappings, and applies these insights to problems in geometry, Painlevé equations, and Schrödinger operators.
Contribution
It establishes a novel analogy between pseudo-Anosov dynamics and Hénon mappings, advancing understanding in geometric and integrable systems.
Findings
Pseudo-Anosov dynamics resemble Hénon mappings
Applied analogy to open questions in geometry and differential equations
Provided new insights into discrete Schrödinger operators
Abstract
We study the dynamics of mapping class groups on 2-dimensional character varieties. We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of H\'enon mappings, and then apply this idea to answer open questions concerning the geometry of discrete and faithful representations, Painlev\'e sixth equation, and discrete Schroedinger operators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
