Polynomial integrability of natural two-dimensional Hamiltonian systems and applications

• Applicant: Professor Dr. Vladimir Matveev
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 455806247

Our project deals with integrable Hamiltonian systems with two degrees of freedom. We study the existence of integrals which are polynomial in momenta. We intend to apply new developed methods in order to construct new phyiscally interesting examples of such systems and tackle a number of famous conjectures. In particular, we plan to solve two conjectures attributed to Birkhoff and the problem of Whittaker. We aim to study the natural generalisations of such systems for magnetic flows and apply obtained results in Finsler geometry and general relativity. Further, we study integrability of magnetic and Finsler billiards.

• DFG Programme: Research Grants
• International Connection: Israel
• International Co-Applicant: Professor Dr. Michael Bialy