Details

Autor(en) / Beteiligte

• KALOSHIN, VADIM
• SORRENTINO, ALFONSO

Titel

Inverse problems and rigidity questions in billiard dynamics

Ist Teil von

• Ergodic theory and dynamical systems, 2022-03, Vol.42 (3), p.1023-1056

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• A Birkhoff billiard is a system describing the inertial motion of a point mass inside a strictly convex planar domain, with elastic reflections at the boundary. The study of the associated dynamics is profoundly intertwined with the geometric properties of the domain: while it is evident how the shape determines the dynamics, a more subtle and difficult question is the extent to which the knowledge of the dynamics allows one to reconstruct the shape of the domain. This translates into many intriguing inverse problems and unanswered rigidity questions, which have been the focus of very active research in recent decades. In this paper we describe some of these questions, along with their connection to other problems in analysis and geometry, with particular emphasis on recent results obtained by the authors and their collaborators.