Reeb Flows with Symmetries: Dynamics and Topology

• Applicant: Dr. Murat Saglam
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 568330991

The aim of this project is to study Reeb flows with symmetries in order to address fundamental questions in low-dimensional conservative dynamics as well as in contact topology in higher dimensions. The project consists of two main branches. The first branch is concerned with three-dimensional Reeb flows, where symmetry means the existence of an invariant function of Morse-Bott type. Our objective here is twofold. On one side we want to understand contact topological obstructions on the existence of such flows as well as on the topological and quantitative aspects of their dynamics. On the other side we want to address recent questions on the entropy of Reeb flows that arise in the context of a question of Katok on the existence of conservative there dimensional flows with vanishing entropy that do not arise as limits of integrable systems. The second branch is concerned with prequantization spaces, on which the standard Reeb flow defines a principal circle bundle structure over a symplectic manifold. The aim here is to study mapping classes of contactomorphisms of prequantization spaces by means of their strict contactomorphisms, especially within the context of recent developments on the question of the orderability of contact structures and the existence of translated points for contactomorphisms.

• DFG Programme: Research Grants