Stable ergodicity of partially hyperbolic symplectomorphisms
报告人：Amie Wilkinson (University of Chicago, US)
时间：2026-05-28 23:00-24:00 (Beijing Time)
地点：Zoom (Online)
Abstract: Symplectomorphisms preserve volume, but their ergodic behavior can be governed by very different mechanisms: Anosov systems are stably ergodic by the Hopf argument, while KAM tori give stable obstructions to ergodicity in high regularity. Partially hyperbolic symplectomorphisms lie between these two regimes. I will discuss the problem of whether stable ergodicity is dense in the space PHS^r of C^r partially hyperbolic symplectomorphisms. On the center-bunched locus, for r>1, previous work of Dolgopyat–Wilkinson and Burns–Wilkinson gives a C^1-dense set of C^1-stably ergodic maps. Beyond the center-bunched locus, no open-dense result is known. Earlier, Avila, Bochi, and I proved that ergodicity is C^1-generic in PHS1. I will describe recent work in progress with Avila and Crovisier aiming for a C^r-open (for r sufficiently large) and C^1-dense version of this generic ergodicity mechanism, using a KAM disk together with a symplectic blender-type construction. A guiding example is an Anosov map coupled to a KAM-type standard map, with the center dynamics not necessarily close to the identity.
Zoom Meeting ID: 850 3302 8146
Passcode: 331058
